Tfl 407 

T596 
Copy 1 



ON THE 



Strength,. Elasticity, Ductility, and Resilience 



OF 



MATERIALS OF MACHINE CONSTRUCTION 



By prof. R. H. THURSTON, 



STEVENS INSTITUTE OF TECHNOI.OaY, 



HOBOKEN, N. J 



:r:eij^jd beif-oire the 



AMERICAN SOCIETY OF CIVIL ENGINEERS, NEW YORK. 



PHILADELPHIA: 

MERRIHEW & SON, PRINTERS, 135 NORTH THIRD STREET. 

187'4. 



THE 





T1 



m 



n 



b 




A SCHOOL OF MECHANICAL ENGINEERING, 



FOUNDED BY THE LATE EDWIN A. STEVENS, AT 



\ 





HOBOKEN, N. J. 


^4^" 




HENRY MORTOxX, Ph. D., 


y 






Mrnmsnl fflaier's 


President. 


MACHIHE SHOP. 


SHOP. 

STEREOPTICONS, 


ALFRED M. MAYER, Ph. D., 

Prof. Physics. 

ROB'T H. THURSTON, A. M., C. E., 
Prof. Mech. Engineering. 


U&CHIHES 

FOR 


Vertical Lanterns, 


dk volson wood, c. e., 


Testing Materials, 


MICROSCOPES, 


Prof. Math, and Mechanics. 


APPARATUS 


spectroscopes, 
B!ow-pipe Apparatus, 


C. W. McCORD, A. M., 

Prof. Mech. Drawing. 

AT.BERT R. LEEDS, A. M., 


FOR 

Testing Lubricants. 


and other kinds of 

Philosophical Apparatos 


Prof. Chemistry. 

CHARLES F: KROEGH, A. M., 

Pi of. Languages. 


A limited amount of spe- 
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on special order. 


MADE TO ORDER. 


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Prof. Belles-lettres. 


Terms, Cash with Order. 



A MECHANICAL LABOMTOEY 

has been founded in connection with the 

DEPARTMENT OF ENGINEERING, 

in which Materials are Tested, and every kind of Technical Research is conducted, 
with the aid of the several other Laboratories of the Institute. Trials of Machinery, 
of Steam and other Engines, and of Steam Boilers, are made under the direction of 
the Professor of Engineering and Director of the Laboratory. 

A small amount of work in designing ma«-hinery and in general engineering can 
be done when it may be made a means of instruction of advanced students. 

For information relating to the work of the Mechanical Laboratory, address the 
Director. 

For information relating to the Course of Instruction, address the President, 

HENRY MORTON, 

-Hoboken, N". J. 



■[From the Journal of the Franklin Institute, April, 1874.] 



m THE STRENGTH, ELASTICITY, DUCTILITY AND RESILIENCE 
OF MATERIALS OF MACHINE CONSTRUCTION, 

And on Various Hitherto Unobserved Phenomena^ Noticed during Experimental Researches 
with a New Testing Machine^ fitted with an Autographic Registry. 

By Prof. R. H. Thurston. 

h 



Eead before American Society of Civil Engineers, Feb. 4, 1874. 



Section I. 

1. Introductory.^ — Some months ago, while engaged with the 
^advanced classes of the Stevens Institute of Technology, in experi- 
mentaPinvestigations of the resistance of materials, it was found that 
-coefficients were given, by various authorities, which neither accorded 
fully with each other or with those then obtained. 

The desirability of determining how far these differences were due 
to errors of observation, and how far to variation in the quality of 
the materials examined, induced the writer to design several machines 
for the purpose of conducting with them a more extended and exact 
series of experiments. The machine for measuring torsional resist- 
ance was furnished with an automatic registry, recording a diagram 
which^ is' a reliable and exact representation of all circumstances 
attending the ^distortion and fracture of the specimen. No system 
of personal! observation could probably be devised which could yield 
results either as reliable or as precise as such a system of autogra- 
phic registry, and, as no method previously in use had given simulta- 
neously, and*at every instant during the test, the intensity of the dis- 
torting force and the magnitude of the coincident distortion, it was 
anticipated that the new method of investigation might be fruitful of 
new and, possibly, important results. This expectation, as will be 
«een, has been more than realized. 

* Vide Journal Franklin Institute. 



2. Description of the Apparatus. 
—The machine, as planned by the 
writer, and as built in the instrument 
makers' workshop, at the Stevens' In- 
stitute, is shown in Fig. 1. This form 
is that with which the investigations to 
be described were made. Since its 
construction, in 1872, however, some 
changes and improvements have been 
made in the design to adapt it to gen- 
eral work, and new designs have been 
made for special kinds of work, as for 
wire mills, railroad shops and bridge 
building. 

Two strong wrenches, C E, B D, 
are carried by the frames A A, A' A\ 
and depend from axes which are both 
in the same line, but are not connected 
with each other. The arm, B, of one 

of these wrenches carries a weight, D, at its lower end. The other 

arm, C, is designed to be moved by hand, in the smaller machines, 

and by a gear and pinion, or a worm gear in larger forms of the appa- 

FjG.2 ratus. The heads of the wrenches are made 

^ — ^ms as shown in Fig. 2, the recess, M, being fit- 
ted to take the head, on the end of the test 
pieces, which is usually given the form 
shown in Fig. 4. 





F!G.3 



FiG.4 





A guide curve, F, of such form that its ordinates are precisely pro- 
portional to the torsional moments exerted by the weighted arm, B D, 
while moving up an arc, to which the corresponding abscissas of the 
curve are proportional, is secured to the frame A A^ The pencil 
holder, J, is carried on this arm, B D, and as the latter is forced out 
of the vertical position, the pencil is pushed forward by the guide 
curve, its movement being thus made proportionate to the force which,, 



3 

transmitted tlirougli the test piece, produces deflection of the weighted 
arm. This guide line is a curve of sines. The other arm, C E, car- 
ries the cylinder, G, upon which the pnper receiving the record is 
clamped, and the pencil, J, makes its mark on the table thus pro- 
vided. This table having a motion, relatively to the pencil, which is 
precisely the angular relative motion of the two extremities of the 
tested specimen, the curve described upon the paper is always of such 
form that the ordinate of any point measures the amount of the dis- 
torting force at a certain instant, while its abscissa measures the dis- 
tortion produced at the same instant. The maximum hand, J, is 
sometimes useful as a check upon the record of maximum resistance. 
The convenience of operation, the small cost,* and the portability 
of the machine are hardly less important to the engineer than the 
accuracy, and the extraordinary extent of information obtainable 
by it. 

8. Method of Operation. — The test piece having been given the 
shape and size which are found best suited for the purpose of the 
experiment, and to the capacity of the machine, it is placed in the 
jaws of the two wrenches, each of which takes one of its squared 
ends, and, a force being applied to the handle, B, the strain thrown 
upon the specimen is transmitted through it to the weighted arm, 
B D, causing it to swing about its axis until the weight exerts a mo- 
ment of resistance which equilibrates the applied force. As the mag- 
nitude of the distorting force changes, the position of the weight sim- 
ultaneously changes, and the pencil indicates, at each instant, the 
value of the stress upon the test piece. As the piece yields under 
strains of increasing amount, also, the pencil is carried in the direc- 
tion of the circumference of the cylinder on which its record is made 
and to a distance which is proportional to the amount of distortion, 
i. e., to the " total angle of torsion." ^ As the applied force increases, 
the specimen yields, and finally, rupture occurring, the pencil returns 
to the base line, at a distance from the starting point which measures 
the angle through which the test piece yielded before its fracture bo- 
came complete. 

4. Interpretation of the Diagrams. — It has been shown that 
the vertical scale of the diagrams produced is a scale of torsional 
moments, and that the horizontal scale is one of total angles of tor- 

* Machines of the size of that used in these experiments, but of improved 
design, are made at the Stevens Institute, at prices as low as $150. 



sion. Since the resistance to shearing, in a homogeneous material, 
varies with the resistance to longitudinal stress, it follows that the 
vertical scale is also, for such materials, a scale of direct resistance, 
and that, with approximately homogeneous substances, this scale is 
approximately accurate, where, as here, all specimens compared are 
of the same dimensions. Since the elasticity of the material is meas- 
ured by the ratio of the distorting force, to the degree of temporary 
distortion produced, the diagrams obtained will exhibit the elastic 
properties of the material, as well as measure its ductility and its 
resilience. 

Referring to the diagrams shown in the accompanying plates, it 
will be noticed that the first portion of the line is a curve of small 
radius, convex toward the axis of abscissas, and that the line then 
rises at a slight inclination from the vertical, but becoming very nearly 
straight, until, at a point some distance above the origin, it takes a 
reversed curvature. The first portion of the line is probably formed 
by the yielding of the loosely fitted packing pieces securing the heads 
of the specimen, and, after they have taken a bearing, by the early 
yielding, in some materials, of particles already overstrained. When 
a firm hold is obtained, the line becomes sometimes nearly straight, 
and the amount of distortion is seen to be approximately proportional 
to the distorting force, illustrating " Hooke's law," Ut tensis sic vis. 

After a degree of distortion which is determined by the specific 
character of each piece, the line becomes curved, the change of form 
having a rate of increase which varies more rapidly than the applied 
force. When this change commences, it seems probable that the mol- 
ecules, which, up to that point, retain generally their original distri- 
bution, while varying their relative distances, begin to change their 
positions with respect to each other, moving upon each other in a 
manner similar, probably, to that action described by Mon. Tresca, 
and called the "Flow of Solids,"* and to which attention has already 
been called by Prof. J. Thompson. f 

It is this point, at which the line commences to become concave 
toward the base, that is considered to mark the '''•lionit of elasticity.'' 
it will be noticed that it is well defined in experiments upon woods, 
IS less marked, but still well defined in the ''fibrous" irons and the 
less homogeneous specimens of other metals, and becomes quite inde- 
tiiminable with the most homogeneous materials, as with the best 

-'^L'Ecoulement des Corps Sohdes ; Paris, 1869, 1871. 

t Cambridge and Dublin Mathematical Journal, Yol. Ill, 1848, pp. 252 — 266. 



qualities of vrell worked cast-steel. This point does not indicate the 
first "set," since, as will be hereafter seen, a set is found to occur, 
either temporary or permanent, and usually partly temporary and 
partly permanent, with every degree of distortion, however small. It 
is at this " elastic limit " that the set begins to become considerable 
in amount and almost wholly permanent. 

The inclination of the straight portion of the line from the vertical 

measures the stiffness of the specimen, the quantity Cot. 6 = ^^ ^ 

being the ratio of the distorting force to the amount of distortion up 
to the " limit of elasticity." As it would seem from the results of 
experiment, as well as of deduction, that this rigidity is very closely, 
if not precisely, proportional to the hardness, in homogeneous sub- 
stances, this quantity Cot. 6 may be taken, for practical purposes, as 
a measure of the hardness of the metals, as well as of their elastic 
resistance to compression. 

After passing the elastic iimit, the line becomes more and more 
nearly parallel to the base line, and then, with the woods invariably, 
and in some cases with the metals, begins to fall rapidly before frac- 
ture becomes evident in the specimen. Where the rising portion of 
the line turns and becomes nearly parallel with the axis of abscissas, 
the viscosity of the material is such that the outer particles "flow" ^ 
upon those within, and, while themselves still offering maximum resist- 
ance, permit molecules nearer the axis to also resist with approxi- 
mately maximum force. It seems probable that, with the more duc- 
tile substances, nearly all are brought up to a maximum in resistance 
before fracture occurs, and this circumstance will be seen hereafter 
to have an important influence in determining the resistance to rup- 
ture. The hardest and most brittle materials break, with a snap, 
before any such flow becomes perceivable, and before the line of the 
diagram commences to deviate, in the slightest degree, from the direc- 
tion taken at the beginning, and before the approach to the elastic 
limit is indicated. It is evident that the standard formulas for tor- 
sional, as well as for other forms of resistance, cannot be perfectly 
correct, since they do not exhibit this difference in the character of 
the resistance offered by ductile and by rigid materials. 

The elasticity of the material is determined by relaxing the distort- 
ing force, at intervals, and allowing the specimen to relieve itself 
from distortion so far as its elasticity will permit. In such cases, the 
pencil will be found to have traced a line resembling, in its general 



6 

form and position, in respect to the coordinates, that forming the 
initial portion of the diagram, but almost absolutely straight, and 
more- nearly vertical. The degree of inclination of this line indicated 
the elasticity, precisely as the initial straight line was made to give a 
measure of the original stiffness of the test piece, the cotangent of 

the angle made with the vertical, Cot. = jf, ^^ beins; the ratio of 

° Tan. (P ° 

the force required to spring the piece through the range recoverable 
by elasticity, to the magnitude of that range. The fact, to be shown, 
that this value is always greater than Cot 0, for the same metal is 
evidence that more or less permanent set will always occur, and that 
the original stiffness of the specimen is always modified, whatever the 
magnitude of the applied force. The form of the line of elastic 
change indicates also the character of the molecular action produc- 
ing it. 

Finally, the form of the curve after passing the maximum, or after 
passing the point at which fracture commences, exhibits the method 
of variation of strength during the process of fracture. This por- 
tion is very difficult to obtain, with even approximate accuracy, with 
any but the toughest and most ductile materials. This terminal por- 
tion of the diagram would be, theoretically, a cubic parabola, the loss 
of resisting power varying with the progressive rupture of concentric 
layers, and the remaining unbroken cylindrical portion becoming 
smaller and smaller until resistance vanishes with the fracture of the 
axial line. In some cases, the curves obtained from ductile metals 
exhibit this parabolic line very distinctly. In all hard materials, the 
jar produced by the sudden rupture of surface particles is suffi- 
cient to separate those within, and the terminal line is straight and 
vertical. 

The homogeneity of the material tested is frequently hardly less 
important than its strength, and it is very desirable to obtain evidence 
which may enable the experimenter to determine the value of tests 
of samples as indicative of the character of the lot from which the 
specimens may have been taken. If the specimens are found to be 
perfectly homogeneous, it may be assumed with confidence that they 
represent accurately the whole lot. If the samples are irregular in 
structure and in strength, no reliable judgment of the value of the lot 
can be based. upon their character, and there can be no assurance that, 
among the pieces accepted, there may not be untrustworthy material 
which may possibly be placed just where it is most important to have 



"the best. It is evident that the more homogeneous a material, the 
more regularly would changes in its resistance take place, and the 
smoother and more symmetrical would be the diagram. The depres- 
sion of the line immediately after passing the elastic limit exhibits 
the greater or less homogeneousness of the material. The fact is 
illustrated in a striking manner in some of the curves presented, and 
we thus have — what had never, I believe, been before found — this 
method of determining homogeneousness. 

The resilience of the specimen is measured by the area included 
within its curve, this being the product of the mean force exerted 
dnto the distance through which it acts in producing rupture, i. g., it 
is proportional to the work done by the test piece in resisting frac- 
ture, and represents the value of the material for resisting shock. 
The area taken within the ordinate of the limit of elasticity, meas- 
ures the capacity for resisting shock without serious distortion or inju- 
:rious set. 

The ductility of the specimen is deduced from the value of the 
"total angle of torsion, and the measure is the elongation of a line of 
surface particles, originally parallel to the axis, which line assumes a 
helical form as the test piece yields, and finally parts at or near the 
point where the maximum resistance is formed. Its value is given on 
Plates II and III for each ten degrees of arc. Since, in this case, 
there is no appreciable reduction of section, or change of form, in the 
specimen, this value of elongation is our actual measure of the max- 
imum ductility of the material, and is an even more accurate indica- 
'tion than the area of fractured cross section as usually measured after 
rupture by tension. It is to be understood that wherever compari- 
sons are here made, without the express statement of other condi- 
tions, that specimens of the same dimensions are always represented 
in the diagrams. 

5. Description of Illustrated Diagrams. The Woods.* — 
Plates I and II exhibit sets of curves which illustrate the general 
characteristics of a large number of materials, the first showing the 
peculiarities noted during experiments on the woods, and the second 
giving an interesting comparison of the metals. 

*The section describing the woods is partly similar to that previously pub- 
lished in the "Journal of the Franklin Institute," and is here reprinted, to pre- 
serve the 'present more elaborate treatise unbroken, and because the study of the 
. several plates, and their comparison was considered essential to a thorough 
^understanding of the subject. — Ed. 



8 

The woods experimented upon were the following, the numbers of 
the respective curves on Plate I, indicating the material here corres- 
pondingly marked : 

1. White pine [Pinus Strohus). 

2. Southern pine [Pinus Australis), sap wood. 

3. Southern pine, heartwood. 

4. Black spruce [Abies Nigra), 

5. Ash [Fraxinus Americanus). 

6. Black walnut [Juglans Nigra). 

7. Red cedar [Juniperus Virginianus). 

8. Spanish mahogany [Swietenia Mahogani), 

9. White oak [Quercus Alba), 

10. Hickory [Carya Alba). 

11. Locust [Robinia Pseudo- acacia). 

12. Chestnut [Castanea Vesca). 

The specimens were all of the form shown in Fig. 3, three and? 
three-fourths inches long, with a diameter of neck of seven-eighths 
of an inch. 

It will be noticed that, in all cases, at the commencement of the 
line, it rises, at a slight inclination from the vertical, and almost per- 
fectly straight. This confirmation of Hooke's law, within the limit 
of elasticity, is best shown in the detached portion a, a, a, of the 
curve obtained with locust, in which the horizontal scale is somewhat 
magnified. The distortion is seen to be very precisely proportional 
to the distorting force, until the law changes at the limit of elasticity. 

It will be observed that, in the larger number of cases, the tor- 
sional resistance increases with great regularity nearly to the angle 
of maximum stress where, suddenly, this rapid rate of increase ceases, 
and the limit of elastic resistance being passed, resistance diminishes 
rapidly with further increase of angular movement, until it becomes 
zero. In the tougher and more dense varieties, this decrease of re- 
sistance occurs less slowly, and in some cases only disappears after a 
large angle of torsion is recorded. In the curves of exceptionally 
strong and tough woods, in which there is known to exist a great ex- 
cess of longitudinal over lateral cohesion, as in those of black walnut 
6, 6, locust 11, 11, and espejsially in those of hickory 10, 10, a pecu- 
liarity is perceivable which is somewhat remarkable, and which is 
especially important in a connection to be hereafter referred to at 
length. 

In these instances the resistance is proportional to the amount of 



9 

torsion, until a maximum is reached, the line then falls as torsioa- 
continues, until a minimum is passed, the curve then again rising and: 
passing another maximum before finally commencing an unintermitted 
descent to the axis of abscissas. Where the difi"erence between lon- 
gitudinal and lateral cohesion is exceptionally great, the second max- 
imum may, as illustrated, for example, by the line described in re- 
cording the test of hickory, have a higher value even than the first. 
This interesting and previously unanticipated peculiarity was shown, 
by careful observation, to be due to the sudden yielding of lateral 
cohesion when the torsional moment reached the value indicated by 
the first minimum. The fibres being thus loosened from each other,, 
this loose bundle of filaments yielded readily, until, by lateral crowd- 
ing as they assumed a helical form and enwrapped each other, their 
slipping upon each other was gradually checked, and resistance again 
commenced increasing. 

At the second maximum, yielding again began in consequence of 
the breaking of fibres under the longitudinal stress measured by that 
component of torsional force having a direction parallel with the fila- 
ments in their new positions, the exterior surface threads parting first 
under this tensile stress, and rupture progressing by the yielding of 
layer after layer, until the axial line being reached, resistance van- 
ished. In this case, rupture seems never to occur by true shearing 
along one defined transverse plane. This feature of depression in the 
curve, occurring as described, is therefore the indication of a lack of 
symmetry in the distribution of resisting forces. It is evident that, 
it may occur either by a difference in the value of cohesive force in 
the lateral and longitudinal directions, or by the structural defects of 
a specimen in which the substance itself may be endowed with cohe- 
sion of equal intensity in all directions. 

The curves shown in Plate I exhibit well the relative values of these- 
materials for the various purposes of the engineer. 

White pine, 1, 1, 1, is shown by the considerable inclination of the 
line of stifi'ness from the vertical, to be soft and deficient in rigidity.. 
The limit of elasticity is quickly reached, and the maximum resist- 
ance of the specimen is found at 15J foot-pounds of moment. Rap- 
idly losing strength after passing the limit of resistance, it is entirely 
broken ofi" at an angle of 130°. The small area comprised by the- 
diagram proves its deficiency of resistance, and its inability to sus- 
tain shock. 

Yellow pine, 2, 2, 2, 3, 3, 3, far excels the first in all valuable pro- 



10 

perties shown by the curve. The sapwood seems, in the specimens 
tested, equally stiff with the heart, but it reaches the elastic limit 
^sooner. The general form of the diagram is the same in both, and 
is characteristically different from that of the white pine. It evidently 
has great value wherever rigidity, strength, toughness and resilience 
are desired in combination with lightness, the latter most important 
quality, together with their cheapness, aiding the qualities here shown 
in determining the application of these woods so extensively for gen- 
eral purposes. It should be noted that, since all comparisons of 
strength are based on measures of volume, a comparison of densities 
should usually be obtained to assist the judgment in making a choice 
from among materials of which tests have been made. 

Spruce, 4, 4, 4, while possessing far less stiffness than even white 
ipine, excels it somewhat in strength, passing its maximum at 18 foot- 
pounds, and submitting to a torsion of nearly 200°. It is proven to 
possess proportionally greater resilience also. It is, however, far in- 
ferior to the yellow pine in every respect. 

Ash, 5, 5, 5, is more deticient in strength and toaghness than is 
generally supposed, and rapidly loses its power of resistance after 
passing the maximum, which point is found at about 27J foot-pounds. 
These specimens may have been of exceptionally poor quality, or, 
possibly, were over-seasoned. 

Black walnut, 6, 6, 6, is remarkably stiff, strong and resilient, its 
diagram resembling somewhat that of oak in general form and dimen- 
sions. The maximum of resistance reaches 35 foot-pounds, and the 
most ductile specimen was only broken off after yielding through an 
arc of 220°. Its stiffness is shown by the fact that it required a mo- 
ment of 25 foot-pounds to spring it 10°, yellow pine requiring but 22 
foot-pounds and spruce but 8, to give them the same amount of dis- 
tortion. 

Red cedar, 7, 7, 7, is very stiff, but is brittle and deficient in strength, 
'breaking off at 92^^, and having a maximum power of resistance of but 
20J foot-pounds. It is, however, one of the stiffest of the woods, its 
specimen requiring 29 foot-pounds of torsional moment to produce a 
total angle of torsion of but 5°. 

Spanish mahogany, 8, 8, 8, is both strong and stiff, bearing a stress 
of 44 foot-pounds, and requiring 32 to produce torsion of 10°. 

White oak, 9, 9, 9, exhibits less strength than either good mahog- 
any, locust or hickory, but it is exceedingly tough and resilient. 
Passing the maximum at an angle of 15°, under a torsional stress of 



11 

B5J foot-pounds, it retains its power of resistance nearly unimpaired 
up to about 70°, and then slowly yields until it suddenly gives way, 
after passing the angle 250°, under a strain due to 9 foot-pounds, and 
breaks off completely at 253°. This strength, toughness and endur- 
ance, under strains due to impact, may be attributed to its consider- 
able lateral cohesion, and to the interlacing of its tenacious fibres, 
which gives this wood its '' cross " grain. 

Hickory, 10, 10, 10, has the highest maximum found during these 
experiments, the second of the pair of maxima already referred to 
being considerably above the maximum of locust even. This speci- 
men exhibits well the ^veil-known valuable properties of the material, 
requiring 45 foot-pounds to twist it 10°, reaching a limit of elasticity 
at 54 foot-pounds and 13°, and having a maximum resisting moment 
of 59J foot-pounds. When it finally yields, it does so quite rapidly, 
breaking off at 145°. 

Locust, 11, 11, 11, gives an excellent diagram. It is the stiffest of 
all, yielding but 10°- at its maximum of 55 foot-pounds, and one piece, 
which was unusually hard and compact, requiring 48 foot-pounds 
to distort it 4°, and reaching a maximum angle of torsion of nearly 
190°. 

It was noticed, during this series of experiments, that different 
specimens of the same species of wood usually exhibited very nearly 
equar strength and rigidity, and that marked differences were only 
-occasionally noted in elasticity and resilience. 

6. The Metals, and the Curves produced by them. — Plate II 
-exhibits a series of curves which illustrate well the general characteris- 
tics and the peculiarities of representative specimens of the principal 
varieties of useful metals. In some cases two specimens have been 
-chosen for illustration, of which one presents the average quality, 
while the other is the best and most characteristic of its class. 

The diagrams obtained by testing metals are quite different in gen- 
eral character from those registered in experiments on the woods, yet 
there are some points of resemblance which it will be instructive to 
notice, since these similar characteristics indicate similar properties 
of the two materials, and a comparison aids greatly in the interpre- 
tation of the diagrams. The woods have a structure w^hich differs, 
in a distinguishing degree, both in the distribution of the substance 
and in the action of these molecular forces capable of resisting rup- 
ture, from that of the metals, the latter being far more homogeneous, 
in both respects, than the former. Wood consists of an aggregation 



12 

of strong fibres, lying parallel, or approximately so, and held toge- 
ther often by a comparatively feeble force of lateral cohesion. The 
latter force being, as often happens, destroyed, the mass becomes a 
collection of loose threads having the general character of a rope or 
cord, with slight or no twist. The metals, on the other hand, are 
naturally homogeneous, both in structure and in the distribution and 
intensity of the molecular forces. Weil-worked and thoroughly an- 
nealed cast-steel, as an example, is equally strong in all directions, is- 
perfectly uniform in its structural character, and is almost absolutely 
homogeneous as to, strain. It would be expected, therefore, that the 
diagrams obtained by breaking such a material would differ from those 
of the woods, in having a smoother and more regular form, and this 
is shown to be actually the case by observation of the curves of cast- 
steel, cast-iron, bronze and others of the more homogeneous metals 
and alloys. 

Some of the metals, it will be noticed, yield diagrams of less regu- 
lar form. Wrought iron, as usually made, has a somewhat fibrous 
structure, which is produced by particles of cinder, originally left in 
the mass by the imperfect work of the puddler while forming the ball 
of sponge in his furnace, and which, not having been removed by the 
squeezers or by hammering the puddle ball, are, by the subsequent 
process of rolling, drawn out into long lines of non-cohering matter, 
and produce an effect upon the mass of metal which makes its beha" 
vior, under stress, somewhat similar to that of the stronger and more 
thready kinds of wood. In the low steels, also, in which, in conse- 
quence of the deficiency of manganese accompanying, almost of ne- 
cessity, their low proportion of carbon, this fibrous structure is pro- 
duced by cells and '' bubble holes " in the ingot, refusing to weld up 
in working, and drawing out into long microscopic, or less than micro- 
scopic, capillary openings. 

In consequence of this structure we find, as we should have antici- 
pated, a depression interrupting the regularity of their curves, imme- 
diately after passing the limit of elasticity, precisely as the same in- 
dication of the lack of homogeneousness of structure was seen in the 
diagrams produced by locust and hickory. 

The presence of internal strain constitutes an essential peculiarity 
of the metals which distinguishes them from organic materials. The 
latter are built up by the action of molecular forces, and their parti- 
cles assume naturally, and probably invariably, positions of equilib- 
rium as to strain. The same is true of naturally formed organic sub- 



13 

stances. The metals, however, are given form by external and arti- 
ficially produced forces. Their molecules are compelled to assume 
certain relative positions, and those positions may be those of equi- 
librium, or they may be such as to strain the cohesive forces to the 
very limit of their reach. It even frequently happens, in large masses, 
thut these internal strains actually result in rupture of portions of 
the material at various points, while in other places the particles are 
either strongly compressed, or are on the verge of complete separation 
by tension. This peculiar condition must evidently be of serious im- 
portance, where the metal is brittle, as is illustrated by the behavior 
of cast-iron, and particularly in ordnance. Even in ductile metals it 
must evidently produce a reduction in the power of the material to 
resist external forces. This condition of internal strain may be re- 
lieved by annealing hammered and rolled metals, and by cooling cast- 
ings very slowly, in order that the particles may assume, naturally, 
positions of equilibrium. In tough and ductile metals, internal strain 
may be removed by heating to a high temperature and then cooling 
under the action of a force approximately equal to the elastic resist- 
ance of the substance. This process, called " Thermo-tension," was 
first used by Professor Johnson in the course of his experiments as a 
member of a Committee of the Franklin Institute, in 1836,* and the 
effect of this action in apparently strengthening the bars so treated, 
was stated in the report of the committee. The fact that this effect 
was very different with different kinds of iron was also noted, but it 
does not appear that the cause of this, which they term " an anoma- 
lous " condition of the metal was discovered by them. 

Metals which are very ductile may frequently be relieved of inter- 
nal strain, also, by simply straining them while cold to the elastic 
limit, and thus dragging all their particles into extreme positions of 
tension, from which, when released from strain, they may all spring 
back into their natural and unstrained positions of equilibrium. This 
fact, which does not seem to have been previously discovered by in- 
vestigators of this subject, will be seen to have an important bearing 
upon the resisting power of materials, and upon the character of all 
formulas in which it may be attempted to embody accurately the law 
of resistance of such materials to distorting or breaking strain. 

Since straining the piece to the limit of elasticity brings all parti- 
cles subject to this internal strain into a similar condition, as to strain, 
with adjacent particles, it is evident that indications of the existence 

* Journal Franklin Institute, 1836-7. 



14 

of internal strain, and through such indications a knowledge of the 
value of the specimen, as effected by this condition, must be sought 
in the diagram, before the sharp change of direction which usually 
marks the position of the limit of elasticity is reached. As already 
seen, the initial portion of the diagram, when the material is free 
from internal strain, is a straight line up to the limit of elasticity. A 
careful observation of the tests of materials of various qualities, 
while under test, has shown that, as would, from considerations to be 
stated nK)re fully hereafter, in treating of the theory of rupture, be 
expected, this line, with strained materials^ becomes convex towards 
the base line, and the form of the curve, as will be shown, is parabolic. 
The initial portion of the diagram, therefore, determines readily 
whether the material tested has been subjected to internal strain, or 
whether it is homogeneous as to strain. This is exhibited by the 
direction of this part of the line as well as by its form. The exist- 
ence of internal strain causes a loss of stiffness, which is shown by 
the deviation of this part of the line from the vertical to a degree 
which becomes observable by comparing its inclination with that of 
the line of elastic resistance, obtained by relaxing the distorting force 
— i. e., the difference in inclination of the initial line of the diagram 
and the lines of elastic resistance, e, e, e, indicates the amount of ex- 
isting internal strains. 

Forged Iron. — In Plate II, the curves numbered 6, 1, 22 and 100 
are the diagrams produced by three characteristic grades of wrought- 
iron. The first is a quality of English iron, well known in our mar- 
ket as a superior metal. The second is one of the finest known brands 
of American iron, and the third is also of American make, but it does 
not usually come into the market in competition with well-known 
irons, in consequence of the high price which is consequent upon the 
necessary employment of an unusual amount of labor, in securing its 
extraordinarily high character. 

No. 6 at first yields rapidly under moderate force, only about 50 
foot-pounds of torsional moment being required to twist at 5°. It 
then rapidly becomes more rigid, as the internal strains, so plainly 
indicated, are lost in this change of form, and at 6° of torsion, the 
resistance becomes 60 foot-pounds, as measured at a. Here the elas- 
tic limit is reached. The next 3° produce no increase of resistance. 
The fact shows that this iron, which was not homogeneous as to strain, 
is nbo not homogeneous in structure. We conclude that it must be 



15 

"badly worked and seamy, and that it may have been rolled too cold ;: 
the former is the probable reason of its lack of homogeneous struc- 
ture, the latter gave it its condition of internal strain. After the first 
9° of torsion, resistance steadily rises to a maximum, which is reached! 
only when just on the point of rupture, and the piece finally com- 
mences breaking at 250°, and is entirely broken oiF at 285°. Its 
maximum elongation, whose value is proportionable to the reduction 
of section noted with the standard testing machines, is 0-691. The 
terminal portion of the line, after rupture commences, is not Usually 
accurate as a measure of the relation of the force to the distortion. 
The increase of resistance between the angle 9° and the angle of rup- 
ture is produced by the additional effort in resistance due to the 
"flow" or drawing out of particles, as already indicated, and the pre- 
cise effect of which will be noticed at length in a succeeding section 
relating to the theory of rupture. 

Applying the scale for tension, which in the case of these curves 
was very exactly 24,000 pounds per square inch for each inch meas- 
ured vertically on the diagram, we find that the elastic limit was 
passed under a stress equivalent to a tension of 19,800 pounds per 
square inch, and that the ultimate tenacity was 59,200 pounds per 
square inch. When nearly at the maximum the specimen was relieved 
from stress, the pencil descending to the base line, and the elasticity 
of the piece produced a certain amount of recoil. The angle inter- 
cepted between the foot of this nearly vertical line, c, and the origin 
at 0, measures the set, which is almost entirely permanent. The dis- 
tance measured from the foot of the perpendicular, let fall upon the 
axis of abscissas, from the head of this line to the foot of the line e^ 
measures the elasticity, a7id is iyiversely proportional to the modulus. 
A comparison of the inclination of the line made by the pencil in 
reascending, on the renewal of the strain with the initial line of the 
diagram, gives the indication of the amount of internal strain origi- 
nally existing in the piece. 

It will be noticed that the horizontal movement of the pencil is re- 
commenced at J, under a higher resistance than was recorded before 
the elastic line was formed. In this case the piece had been left 
under strain for some time before the stress was relieved, and the 
peculiarity noted is an example of an increase of resistance under 
stress,* or more properly of the elevation of the elastic limit, of which 
more marked examples will be shown subsequently. 

* Vide Transactions, Yol. II, page 290. 



16 

The exceptional stiffness and limited elastic range here shown, as 
^compared with the other examples given, is probably a phenomenon 
:accompanying and due to this increase of resistance under stress. 

Examining No. 1 in a similar manner, we find that it is far freer 
from internal strain than No. 6, its initial line being much more 
aiearly straight and rising more rapidly. It is rather less homoge- 
neous in structure, and is forced through an arc of 6°, after hav- 
ing passed its elastic limit, before it begins to offer an increas- 
ing resistance. It is evidently a better iron, but less well worked, 
and, as shown by the position of the elastic limit, is somewhat harder 
and stiffer. No. 1 retains its higher resistance quite up to the point 
at which No. 6 received its incidental accession of resistance by stand- 
ing under strain, and the two pieces break at, practically, the same 
point. No. 1 having slightly the greater ductility. When the " elas- 
tic line," e, is formed, just before fracture, it is seen that No. 1 has 
a greater elastic range and a lower modulus than No. 5. It should 
be observed that the line by which the pencil descends to the base 
line has usually no value, owing to the fact that no care is generally 
taken to remove the stress as gradually as it is applied. When such 
<jare is taken, the lines are usually coincident, and do not form the 
loop here seen. It will also be noticed that these lines often cross 
•each other, that on the right being the important line. The elastic 
line formed by No. 1 at between 40° and 45° of torsion is seen to be 
very nearly parallel with that obtained near the terminal portion of 
the diagram, and illustrates the fact here first revealed to the eye, 
that the elasticity of the specimen remains practically unchanged up to 
the point of incipient rupture, and this fact corroborates the deduc- 
tions of Wertheim* and others who came to this conclusion from less 
satisfactory modes of research. All experiments yet made give a 
similar result. 

No. 22 illustrates the characteristics of a metal which probably 
represents one of the best qualities of wrought iron made in this or 
in any other country, and with which every precaution has been taken 
to secure the greatest possible perfection, both in the raw material 
and in its manufacture. The fact that it finds a market at sixteen 
cents a pound proves that even such care and expense are well ap- 
plied. The line of this diagram, starting from 0, rising with hardly 
perceptible variation from its general direction, turns, at the elastic 
limit, a, under a moment of about 80 foot-pounds, equivalent to a 

* Vide Annales de Chimie et de Physique. 



17 

tension of about 24,000 pounds per square inch ; and with between 
2° and 3° of torsion only, and thence continues rising in a curve al- 
most as smooth and regular as if it had been constructed by a skilful 
-draughtsman. Reaching a maximum of resistance to torsion of 220 
foot-pounds and an equivalent tensile resistance of over 66,000 
pounds per square inch, at an angle of 345°, it retains this high re- 
sistance up to the point of rupture some 358^^ from its starting point. 
The maximum elongation of its exterior fibres is 1*2, making them 
at rupture 2*2 times their original length. This would produce a 
probable breaking section in the common testing machine equal to 
0-4545 of the original section. f 

From the beginning to the end this specimen exhibits its superi- 
ority, in all respects, over the less carefully made irons, Nos. 1 and 
6, which, it should be remembered, are themselves deservedly known 
as good brands. The homogeneousness of No. 22 is almost perfect, 
both in regard to strain and to structure, the former being indicated 
by the straightness of the first part of the diagram and its parallel- 
ism with the '* elastic line,'' e, produced at 217J°, and the latter be- 
ing proven by the beautiful accuracy with which the curve follows 
the parabolic path indicated by our theory as that which should be 
produced by a ductile homogeneous material. At similar angles of 
torsion. No. 22 ofi'ers invariably much higher resistance than either 
Nos. 1 or 6, and this superiority, uniting with its much greater duc- 
tility, indicates an immensely greater resilience. It is evident that 
for many cases, where lightness combined with capacity to carry live 
loads and to resist heavy shocks are the essential requisites, this iron 
would be by far preferable, notwithstanding the cost of its manufac- 
ture, to any of the cheaper grades. Comparing their elasticities, as 
shown at SIO'^, 215°, it is seen that No. 22 is about equally stifi" and 
elastic with No. 1, while both have a wider elastic range and are less 
rigid, and hence are softer than No. 6, whose elastic line is seen at 
221°. All of the characteristics here noted can be accurately gauged 
by measuring the diagrams, and constants are readily obtained for 
all formulas, as illustrated in a later section of this paper, in which 
the construction of formulas and the determination of constants will 
be made the subject of investigation. 

f Compare Kirkaldy : Strength of Iron and Steel; pp. Ill, 135, for reduc- 
tion in Yorkshire and Swedish bars. The elongation there given has, of course, 
DO value as a measure of ductility. 



18 

No. 100 is the curve obtained from a piece of Swedish iron, marked 
. Its characteristics are so well marked that one familiar with 
the metal would hardly fail to select this curve from among those 
of other irons. Its softness and its homogeneous structure are its 
peculiarities. Its curve, at first, coincides perfectly with that of No. 
6. It has, however, slightly less of the condition of internal strain, 
and a somewhat higher limit of elasticity. The elastic limit is found 
at 5J° of torsion, and at a stress of 65 foot-pounds of moment, equiv- 
alent to 19,500 pounds on the square inch, in tension. Its increase 
of resistance, as successive layers are brought to their maximum and 
begin to flow, is very nearly the same as that of the specimens Nos. 
1 and 6, and the line lies between the diagrams given by these irons 
up to 30°, and then falls slightly below the latter. At 220°, it at- 
tains a maximum resisting power, and here the outer surface begins 
to rupture, after an ultimate stretch, of lines formerly parallel to the- 
axis, amounting to 0"564. Had this elongation taken place in the 
direction of strain, as in the usual form of testing machine, it would 
have produced a reduction of section to 0*64, the original area.* At 
this point the stress in tension equivalent to the 176 foot-pounds of 
torsional stress, is 52,800 pounds per square inch. From 250° the 
loss of resistance takes place rapidly, but the actual breaking oflf of 
the specimen did not occur until it had been given a complete revolu- 
tion. This part of the diagram distinguishes the metal from all: 
others, and shows distinctly the exceptionally tough, ductile and ho- 
mogeneous character which gives the Swedish irons their superiority 
in steel making. No. 22, even, although much more extensible, iff 
harder than No. 100, and yields more suddenly when it finally gives 
way. 

A comparison of the results here recorded with those obtained by 
Styffe,t will aiford a good basis upon which to form an idea of the ac- 
curacy as well as the convenience of this method of deriving them. 
An examination of the broken test piece gives some evidence con- 
firmatory of the record. The exterior surface of the twisted portion 
has an appearance intermediate between that of No. 1, Fig. 6,| and 
No. 22, Fig. 7; with an evident tendency to "kink." The surface of 
fracture is lighter and more lead-like than even No. 22, and its 

* Compare Styffe ; Strength of Iron and Steel; p. 133, Nos, 26—30. 

t As on last page. 

X From an article in the " Scientific American," of January 17th, 1874, oni 
Testing the Quality of Iron, Steel and other Metals without Special Appa- 
ratus. • 



liJ 



"fibre " is finer and texture more plastic in appearance. It is beau- 
tifullj uniform in character. On one end of this specimen, where a 
piece had been nicked and then broken ofi" by a sharp blow, the ab- 
sence of all fibrous appearance, and the granular texture and magnifi- 
cently fine, regular grain are very marked, and Fig. 5. 
indicate that the material is entitled to its es- 
Fig. 6. tablished position as 
the purest metal known 
in the market. The 
specimens themselves 
furnish almost as val- 
uable information, af- 
ter test, as the dia- 
grams contain, and 
should always be care- 
fully inspected with a 

view to securing additional or corroborative- 
information. Fig. 5 is a sketch of specimen- 
No. 1, and shows its somewhat granular frac- 
ture, and the seamy structure produced by a 
defective method of working. Fig. 6, from specimen No, 16, more 
nearly resembles that which gave the diagram marked 6. The metal 
is seen to be good, tough, and better in quality than No. 1, but it is 
even more seamy, and even less thoroughly worked, as is evidenced 
by the cracks extending around the neck, and by the irregularly dis- 
tributed flaws seen on its end. 

No. 7 exhibits the appearance of No. 22 after fracture, and shows, 





even more perfectly than the pencilled re- 
cord, the splendid character of the material. 
The surface of the neck was originally 
smoothly turned and polished, and care- 
fully fitted to gauge. Under test it has 
become curiously altered, and has assumed 
a rough, striated appearance, while the 
helical markings extend completely around 
it. The end has the peculiar appearance 
which will be seen to be characteristic of 
tough and ductile metals, and the uniform- 
ly bright appearance of every particle in 
the fractured section shows how all held to- 



Fig. 7. 




20, 

gether up to the instant of rupture, and that fracture finally took 
place by true shearing. Rupture by torsion thus brings to light ev- 
ery defect nnd reveals every excellence in the specimen. Rupture by 
tension rarely reveals more than the mere strength of the material. 

8. — Low Steels. — In Plate II, and above the curves just described, 
are a set obtained during experiments on "low steels," produced by 
the Bessemer and Siemens-Martin processes. In general character, 
the curves are seen to resemble those of the standard irons, as illus- 
trated by Nos. 1 and 6. The irons contain usually barely a trace of 
carbon. These steels contain from one-half to five-eighths of one per 
cent. The irons are made by a process which leaves them more or less 
injured by the presence of impurities, from' which the utmost care 
can seldom free them. The steels are made from metal which has 
been molten and cast, a process which allows a far more complete 
separation of slag and oxides. The low steels, however, are liable to 
an objectionable amount of porosity, due to the liberation of gas while 
the molten mass is solidifying, whenever the spiegeleisen, employed 
as a conveyor of carbon, is not very rich in manganese. The results 
of these differences in constitution and treatment are readily seen by 
inspecting the curves. They show a stiffness equal to No. 6, and 
about the same degree of internal strain. They contain a sufficient 
number of the capillary channels, produced by drawing down the 
pores while working the ingot into bar, to cause a lack of homogene- 
ousness in structure, very similar to that produced in iron by cinder. 
They have a much higher elastic limit, and greater strength, and the 
softer grades have great ductility. In resilience, these softest steels 
excel all other metals, except the unusual example. No. 22,- and are 
evidently the best materials that are now obtainable for all uses where 
a tough, strong, ductile metal is needed to sustain safely heavy shocks. 
A comparison of the diagrams of two competing metals may thus be 
made to indicate how far a difference in price should act as a bar to 
the use of the costlier one. For many purposes, a metal having 
double the resilience of another is worth more than double-price. For 
general purposes, a comparison of the resilience of the metals within 
the elastic limit is of supreme importance. No. 6 is seen to have 
more resilience within this limit than No. 1, and the steels far more 
than either ; but No. 1 would take a set of considerable amount far 
within the true elastic limit, as indicated at a. The most valuable 
measure is obtained by determining the area intercepted between the 



21 

" elastic line " and the perpendicular let fall from its upper end ; this 
measures the resilience of elastic resistance, which is the really im- 
portant quality. 

No. 98 was cut from the head of an English Bessemer rail made 
from unmixed Cumberland ores. It contains nearly 0*4 per cent, 
carbon. It is quite homogeneous, has a limit of elasticity at 88 foot- 
pounds of torsional, or 26,400 pounds per square inch tensile stress, 
approaches its maximum of resistance rapidly, and, at 210'^, the tor- 
sional moment becomes 225 foot-pounds, equivalent to 67,500 pounds 
per square inch tensile stress. It only breaks after a torsion of 283°, 
and with an ultimate elongation of 80 per cent., equivalent to a re- 
duction of cross section to 0*5.56. 

No. 76 is a Siemens-Martin steel made from mixed Lake Superior 
and Iron Mountain ores, and contained about the same amount of car- 
bon as the preceding. It contains rather more phosphorus, which 
probably gives it its somewhat greater hardness, its higher limit of 
elasticity and its somewhat reduced ductility. Its elastic limit is 
found at 104 foot-pounds of torsion, or 31,200 pounds tensile resist- 
ance, and its ultimate strength is almost precisely that of the pre- 
ceding specimen. Its elongation is 0*66 maximum. Unless more 
seriously affected by extreme cold than No. 98, it would be preferred 
for rails, and, perhaps, for most purposes. 

No. 67 is a somewhat " higher '* steel, made by the same process. 
It is less homogeneous than the two just examined, has greater 
strength and a higher elastic limit, but less ductility. Its resilience 
is very nearly the same as that of Nos. 98 and 76. The elasticity of 
all of these steels seems very exactly the same. The ductility of No. 
67 is measured by 0-40 elongation. Aid, is seen another illustration 
of elevation of the elastic limit. The piece was left twenty-four 
hours under maximum stress. The torsional force was then removed 
entirely. On renewing it, as is seen, the resistance of the specimen 
was found increased in a marked degree. 

No. 69 is an American Bessemer steel, containing not far from 0*5 
per cent, carbon. The same effect is seen here that was before noted, 
an increase of hardness, a higher elastic limit, and greater strength, 
obtained, however, by some sacrifice of both ductility and resilience. 
The elastic limit is approached at 130 foot-pounds of torsional moment, 
or 39,000 pounds tensile, and the maximum is 280 foot-pounds of 
moment and 84,000 pounds tensile resistance at 133°. Its maximum 
angle of torsion is 150°, its elongation 0*24. 



22 

No. 85 is a singular illustration of the effects of what is probably a 
peculiar modification of internal strain, it seems to have no charac- 
teristics in common with any other metal examined. Its diagram 
would seem to show a perfect homogeneousness as to strain, and a 
remarkable deficiency of homogeneity in structure. It begins to ex- 
hibit the indications of an elastic limit at a^ under a torsional moment 
of 110 foot-pounds, or an apparent tensile stress of 33,000 pounds 
per square inch, and then rises at once by a beautifully regular curve, 
to very nearly its maximum at 16°, and 176 foot-pounds. The maxi- 
mum is finally reached at 130°, and thence the line slowly falls until 
fracture takes place at 195°. The maximum resistance seems* to be 
very exactly 60,000 pounds to the square inch. Its maximum elon- 
gation for exterior fibres is about 0*23. The resilience taken at the 
elastic limit is far higher than with common iron, and it is seen that 
this metal, in many respects, may compete with steel. Its elasticity 
is seen to remain constant wherever taken. This singular specimen 
was a piece of " cold rolled " iron. It is probably really far from 
homogeneous as to strain, but its artificially produced strains are sym- 
metrically distributed about its axis, and being rendered perfectly 
uniform throughout each of the concentric cylinders into which it may 
be conceived to be divided, the effect, so far as this test, or so far as 
its application as shafting, for example, is concerned, is that of per- 
fect homogeneousness. The apparently great deficiency of homo- 
geneousness in structure is readily explained by an examination of 
the pieces after fracture ; they are fibrous, and have a grain as thread- 
like as oak ; their condition is precisely w^hat is shown by the diagram, 
and the metal itself is as anomalous as its curve. 

8. — Tool Steels. — The " tool steels " differ chemically from the 
^' low steels " in containing a higher percentage of carbon, and usually, 
in being very nearly, if not absolutely, free from all injurious elements. 
They are made in crucibles by melting down the blister steels which 
are the crude product of the process of cementation, or sometimes, by 
melting a charge composed of selected iron, a small proportion of 
manganese bearing alloy and the proper amount of carbon. Contain- 
ing a higher proportion of carbon than the preceding class of metals, 
it is comparatively easy to secure homogeneousness by the introduc- 
tion of manganese, and by the same means, to eliminate very per- 

* With an exceptional case, of which this is an example, the scale for tension 
s incorrect. The tensile strength is probably higher than here given. 



23 

fectly the evil effects of any small proportion of sulphur that may be 
present. Their comparatively large admixture of carbon makes them 
harder, and reduces their ductility, and since the reduction of ductility 
occurs to a greater degree than the increase of strength, the effect is 
also to reduce their resilience. The working of these metals is more 
thorough than is that of the less valuable steels, or of iron. They are 
cast in comparatively small ingots, and are frequently drawn down 
under the hammer, instead of in the rolls, and are thus more com- 
pletely freed from that form of irregularity in structure noticed so 
invariably in steels otherwise treated. The effect of increasing the 
proportion of carbon, is to confer upon iron the property of harden- 
ing, when heated to a high temperature, and suddenly cooling, and 
the invaluable property of " taking a temper," i. e., of assuming, 
under proper treatment, any desired degree of hardness. The hard 
steels are, however, comparatively brittle, the hardening being 
secured at the expense of ductility. The effect produced upon the 
tenacity of unhardened steel, by increasing proportions of carbon, is 
somewhat variable, since it is influenced greatly by the presence of 
other elements. For good steels unhardened, the writer has been 
accustomed to estimate tenacity by the following formula, which is 
approximately accurate, and may be often found useful : 

1^=60,000 + 70,000 0, 
in which T represents the tenacity in pounds per square inch, and 
is the percentage of carbon contained in the metal. This subject will 
be considered at greater length after a series of experiments have 
been made to obtain more exact determinations. 

Referring to Plate II, a set of diagrams will be found, having their 
origin at 180°, which are fac similes of those automatically produced 
during experiments upon various kinds of tool steels. 

Ko. 58 is an English metal, knoAvn in the market as " German 
crucible steel." It is remarkable as having a condition of internal 
strain which has distorted its diagram to such an extent as to com- 
pletely hide the usual indication of the elastic limit. A careful in- 
spection shows what may be taken for this point at about 14:J° of 
torsion, when the twisting moment was about 120 foot-pounds, and 
the tensile resistance 36,000 pounds per square inch. The metal is 
homogeneous in structure, has an ultimate resistance of 302 foot- 
pounds of moment, or 90,600 pounds per square inch tensile resist- 
ance. Its resilience is evidently inferior to that of the softer metals, 
and also less than the next higher and better grades. This metal 



24 

contains about 0*60 to 0-65 per cent, carbon. Its elongation amounts 
to 0-045. 

No. 53 is an English *' double shear steel," of evidently very ex- 
cellent structure, but less strong and less resilient than the preceding. 
Its exterior fibres are drawn out three per cent. 

Nos. 41 and 61 are two specimens of one of the best English too^ 
steels in our market. The first was tested as cut from the bar, but 
the second was carefully annealed before the experiment. In this^ 
instance, annealing has caused a slight loss of resilience as well as a 
decided loss of strength. In No. 41, the limit of elasticity can hardly 
be detected, but seems to be at about the same point as in No. 61, at 
near 130 foot-pounds moment and 39,000 pounds tension. The ulti- 
mate strength is nearly 119,000 pounds per square inch. The pro- 
portion of carbon is very closely 1 per cent. Its section would 
reduce by tension, 0-05. 

No. 70 is an American "spring steel," rather hard, but as showtt 
by its considerable resilience, of excellent quality, resembling remark- 
ably the tool steel No. 41. It differs from the latter, apparently by 
its much higher elastic limit. It is possible that this may have been 
caused by more rapidly cooling after leaving the rolls in which it waa 
last worked. It is evident that, for exact comparison, all specimens- 
should be either equally well annealed or should be tempered in a 
precisely similar manner, and to the same degree. 

Nos. 71 and 82 are American tool steels, containing about 1*15 of 
carbon. The former is notable as having an elastic limit at 69,000- 
pounds, and a probable deficiency of manganese, producing the usual 
indication of heterogeneous structure. Both of these steels lack, 
resilience, and are less well adapted for tools like cold chisels, rock 
drills, and others which are subjected to blows, than for machine tools. 
They have a maximum elongation, respectively, of but 0*013 and 
0-03. 

Interesting and instructive as the study of these curves may be- 
made, the information obtained from them is supplemented, in a most 
valuable manner, by that obtained by the inspection of the fractured 
specimens, upon which the peculiar action of a torsional strain has 
produced an effect in revealing the structure and quality of the metal 
that could be obtained in no other way. 

Fig. 8 represents the appearance of No. 68, and Fig. 9 that of No. 
58, while the peculiarities of the finest tool steels are seen in No. 71^ 



25 



Fig. 8. 



Fig. 9. 





Fig. 10. 




as shown in Fig. 10. The smooth exterior 
of No. 68, which is a companion specimen 
to that giving diagram 69, and its bright 
and characteristic fracture, resembling that 
of No. 22 somewhat, together indicate its 
nature perfectly, the first feature proving 
its strength and uniformity of structure, 
and the second showing, even to the inex- 
perienced eye, its toughness. This is a 
representative specimen of low steels. No. 
58 is seen to have retained, even more than 
No. 68, its original smoothly polished sur- 
face. Its fracture is less waxy, and much 
more irregular and sharply angular. The crack running down the 
side of the neck shows its relationship to the shear steels which much 
oftener exhibit this effect of strain, in consequence of their lamellar 
character. No. 58 is evidently intermediate in its character between 
the soft steels, like No. 68, and the tools steels which are represented 
by No. 71, Fig 10. In this test-piece, the fracture is ragged and 
splintery, and the separated surfaces have a beautifully fine, even 
grain, which proves the excellence of the material. The surface 
which was turned and polished in bringing the metal to size remains 
as perfect as before the specimen was broken. By an inspection of 
the broken test-pieces in this manner, the grade of the steel, and such 
properties also as are not revealed by an examination of the diagram 
of strain, are very exactly ascertained by a novice, and to the practi- 
cal eye, the slightest possible variations are readily distinguishable.. 



26 """"" 

9. Cast-iron. — The diagrams of strain having their commencement 
at 100°, have been obtained from cast-iron and from malleableized 
<3ast iron. 

Nos. 23 and 24 are those given by a good dark grey foundry iron 
from Pennsylvania. No. 25 represents the curve of light grey scrap, 
and 30 is from a very fine white Lake Superior charcoal iron. The 
latter is seen to be exceedingly hard and rigid, the resistance of the 
piece rising very precisely in proportion to the angle of torsion until 
it snaps at last under a moment of over 200 foot-pounds, equivalent 
to a tension of 60,000 pounds per square inch, and with a maximum 
elongation of one-tenth of one per cent. This is a most extraordinary 
resistance, but it is evident that, notwithstanding its immense 
strength, this material would be valueless for ordinary purposes in 
<;onsequence of its excessive brittleness. When the torsional effort 
iiad reached about one-half its maximum amount the piece was re- 
leased. The pencil retreated along a nearly vertical line e, which it 
again traversed as the strain was gradually renewed. Here as in 
many other cases, where a similar experiment was made, evidence is 
given of the truth of the statement originally made by Hodgkinson,* 
that every load produces a set. As will be shown, subsequently, 
however, it is not true in perfectly homogeneous bodies free from 
strain, and within their elastic limit. The light grey iron has a limit 
of elasticity at near one-half the maximum reached by the white iron, 
without any sign of reaching the limit of its elasticity. The grey has 
more ductility than the white iron, but has only about two-thirds the 
resilience of the latter. The dark grey irons are evidently better 
than either of the lighter grades, except in power of carrying an ab- 
solutely static load. The actual stretch of the outer surface particles 
is very nearly the same in all three. They are excellent specimens 
of their class, and considerably better than ordinary irons. 

No. 37 is a " malleableized cast-iron," made from the extraordinary 
metal illustrated in No. 30. The process of malleableizing consists 
in decarbonization by heating the casting made from good white iron, 
in contact with iron oxide or other decarbonizing material. Without 
removing any other constituent than the carbon, it produces a crude 
isteel or an impure wrought-iron. When performed in the usual man- 
ner, melting the cast-iron in a cupola in contact with the fuel, and 
with some flux, and then carrying the process of malleableizing to the 

""■ Reports of British Association ; also Civil Engineer and Architects' 
Journal. 



27 



tisual extent, a metal is obtained such as is illustrated by the diagram 
marked 37. It retains the strength of the cast-iron, and acquires 
some ductility. 

No. 30 yielded 7° before fracture, while No. 37, vastly more 



Fig. 11, 



Fig. 12. 



ductile and resilient, 
only broke after a tor- 
sion of 39°, and a maxi- 
mum elongation of 2 
per cent. Taking the 
precaution to melt the 
iron in an "air furnace" 



— a form of " re verbera- 

tory " — and conducting 

the process of malleable- 

izing more carefully, a 
still more valuable material was obtained. 

No. 35 represents this iron. Its resemblance to wrought-iron, 
both in appearance of fracture and in its strength and ductility, are 





Fig. 14. 



Fig. 13. greatly increased. It 

has a high limit of elas- 
ticity—over 20,000 lbs. 
per square inch — and 
such ductility that it 
only breaks after a tor- 
sion of nearly 168°, and 
^^ an elongation of " fibre" 
of 0-35. It is not very 
^y homogeneous, but it is 
^ as strong, and almost as 
tough, as a good wrcught- 
iron. This material has 
^especial value for many purposes, because of the facility with \^hich 
awkwardly shaped pieces can be made of it. In many cases, it will 
prove as good as wrought-iron and far cheaper. 

Fig. 11 shows the appearance of this last specimen. Its resem- 
blance to wrought-iron is very noticeable. The lines running like 
the thread of a screw around the exterior of the neck, and the smooth 
even fracture in a plane precisely perpendicular to the axis, are the 
instructive features. Fig 12, representing No. 33, is a specimen 
similar in character to No. 37. The comparative lack of ductility, its 





28 

less regular structure, and its less perfect transformation are perfectly 
exhibited. Fig 13 is an excellent cut of the white iron as cast and with- 
out malleableizing. Its surface, where fractured, has the general appear- 
ance of broken tool steel. The color and texture of the metal are 
distinctive, however. It has none of the " steely grain." Fig. 14 
represents the dark grey iron. Its color, its granular structure and 
coarse grain are markedly characteristic, and no one can fail to per- 
ceive, in the specimen, the general character which is exactly given by 
the autographic diagrams of the testing machine. 

10. Other Metals. — The diagrams numbered 87, 88 and 89, are- 
those of copper, tin and zinc. These specimens are all of cast metal, 
carefully selected under the direction of the writer, and molded anJ 
cast at the Stevens Institute of Technology. They exhibit neatly 
the wonderful superiority which the various kinds of iron and steel 
possess over the other useful metals. These metals all take a set 
under very small strains, pass their limits of elasticity at some inde- 
terminable, but evidently low point, and possess very slight tenacity. 

Zinc, No. 89, by the regularity of its curve shows a very uniform 
structure. It increases very gradually in resistance to torsion, until 
it reaches the angle 50°, at which point it has a moment of torsional 
resistance of 36 foot-pounds, and a maximum tenacity of about 10,- 
800 pounds per square inch. It loses its power of resistance, after 
rupture commences, as regularly, but not as slowly, as it acquired it^ 
and rupture becomes complete at 63°. Its resistance is exceedingly 
small, and it is evidently unfit to bear either static or dynamic force. 
Its stretching power has a maximum of 0*04. 

Tin, No. 88, is equally remarkable for its exceedingly feeble resist- 
ance and its great ductility. The specimen was excellent, both in 
quality of metal and in closeness of structure, as was indicated by the 
clearness of the "tin cry " heard while undergoing the test and by 
the fine, smooth, clean fracture. The character of the curve is simi- 
lar to that of zinc, but has far greater extent. Its elastic limit is- 
quite indeterminable. The outline of the diagram indicates very per- 
fect homogeneousness. The maximum resistance to torsion is found 
at 240°, and under a stress of 19 foot-pounds. Its tenacity deduced 
from the diagram is, at most, but 5,700 pounds per square inch. 
Rupture occurs very gradually, and the piece separated entirely at 
355°. Notwithstanding its great ductility, its low tenacity producer 
a low resilience, although in this quality it excels zinc, which latter 



29 

metal had nearly double its strength. Its elongation by tension 
would have reduced its section to 0-6 of the original cross area, if that 
reduction were proportional to the ductility shown by the diagram. 

Copper, No. 87, cast in green sand, like the zinc and tin just de- 
scribed, was found, on examination of the fracture, to differ from 
them in being exceedingly porous. The effect of this fault has been 
to weaken it seriously. Its curve closely resembles that of zinc, but 
is abruptly terminated by the piece suddenly breaking off at 46°. It 
reaches a maximum sooner than zinc, at 29^, and its greatest resist- 
ance to torsion is 36 foot-pounds, or to tension 10,800 pounds per 
square inch, precisely the same as zinc. Its ductility has a value of 
one and a half per cent. Its resilience is somewhat less than that of 
zinc. Its limit of elasticity is diflBcult to determine, but has been 
taken at 1J° where the moment of resistance is 13 foot-pounds, 
equivalent very nearly to 3,900 pounds tenacity, per square inch. 

No. 134 is the curve of cast copper, precisely similar to No. 87, 
but cast in a dry sand mold. The marked difference between these 
specimens is probably due, not only to the difference in degree of 
porosity which arises from the presence of vapor, which permeates 
the casting in one case, filling it with bubble holes, and which is al- 
most unobservable in the last, but the slower cooling of the dry sand 
casting also probably produces its effect in strengthening the metal. 
This last specimen has a limit of elasticity at not far from 13f °, and 
under a torsional stress equivalent to a tension of 5,400 pounds per 
square inch. The maximum values of these quantities are found at 
21^, and are 42 foot pounds, and 12,600 pounds per square inch re- 
spectively. The resilience of the specimen is much greater than that 
of the preceding, and its maximum elongation is -026. Altogether, 
this is far betterthan the preceding, and it would seem that copper, 
and probably all its alloys, should, when possible, be cast in dry 
sand, to secure density and strength. 

No. 141 is a piece of forged copper, hammered into a one-inch 
square bar, from a piece originally 3J inches wide and j inch thick. 
The most striking property noticed is its immense ductility, far ex- 
ceeding that of any other piece of metal yet tested, and, in amount, 
many times as great as the cast metal. Its limit of elasticity is 
reached very quickly, although it is impossible to say precisely where 
it occurs. Comparing its " elastic line " with the initial portion of 
the curve, it is seen that the slightest force produces a set which is 
proportionally large as compared with the sets of other metals. The 



30 



m Zl 96 rj' '![ ' ''*"' ^"^'^ °f *°^^'°" ^'f 450°, and which 
measures 96 foot-pounds moment, or 28,800 pounds per square inch 
Kupture ,s finally obtained after a torsion of 643°. The IxiLut 
elongafon . 210 per cent., the most elongated lines f paSs 
Ho'rl" ' '^'';?'' T ''^'- °"'«'"^' ■^i"'- Had this'ch g 

ve been ::: 32Y.r ""/' ""'°"' '"^^ ^^^"'"-^ "^ -'^'1 
nave been but -323 the area of original section. The resilience of 

t wo'T;r ^'''"," '""^"^'y '"^'«"'«''-' -'^- the lim t Jhieh 
n would be seriously distorted by a blow, but is quite large in amount 
where resistance extends to the point of rupture. This is perftctl 
consonant w.th that knowledge of the material which ever; mecS 

ac^Zt ':;» r P^-"- -'•> :'• Here, however, we have a co^p te 
account of Us properties, written out bj the material itself with 
definite and accurate measures. 

wblJi; ^^T^'' CoNCLCSiONS._These plates, exhibiting the diagrams 
which are the autographs of all the useful metals, illustrate sufficienTlv 
well the remarka le fullness and accuracy with ;hich the r pr^peS 
may be graphically represented, and the convenience with wS hey 
may be studied, with the aid of so simple a recording machin A 
comparison of results deduced as shown, with those obtained s" fat 
as they can be obtained at all, the usual method of simp ypuRin! Z 
specmens asunder, and trusting to, sometimes, unskillW ha ds a„I 
an untrained observer, for the adjustment of weights and the reLtr r 
of results, will indicate the close approximation of this method J 
even ascertaining the behavior of the metal in tension. On examin 

ng the results of the experiments, made by him and by his col 

S;;:' iT'i "^^'■»^' "° ''"^ -" ^^" '° "e struck'with the 

aTlv and twuT fr! *° '''' ''""^^ ^''' produced automati- 
cally, and It will be readily believed that not only must there be verv 
perfect correspondence of results where the two methods are careful v 
compared, but, also, that any theory of rupture must b f S 

hetgiveTanTLT^tr '°* "''''■ ^''-'^-'■o- of the C 

ariTaTiitrtix:^""^^ ''''''' -' '-^ ^- 
anJtrsTsCh^f reT:i:rd^t '-''--' -'-'- 

.enerally, is based up^n a compaS:' 07^*:; rtSTr^irS 



31 

those obtained from the irons by tensile test, by the writer, and is- 
confirmed by a compilation of results given by other experiments on< 
the same brands. 

12. Testing within the limit of Elasticity. — In determining 
the value of materials of construction, it is usually more necessary to 
determine the position of the limit of elasticity and the behavior of the- 
metal within that limit than to ascertain ultimate strength or, except, 
perhaps, for machinery, even the resilience. It is becoming well 
recognized by engineers who are known to scand highest in the pro- 
fession, that it should be possible to test every piece of material which- 
goes into an important structure and to then use it with confidence 
that it has been absolutely proven to be capable of carrying its load 
with a sufficient and known margin of safety. It has quite recently 
become a common practice to test rods to a limit of strain determined 
by specification, and to compel their rejection when found to take a 
considerable permanent set under that strain. The method here 
described allows of this practice with perfect safety. The limit of 
elasticity occurs within the first two or three degrees, and, as seen, 
the specimen may be twisted a hundred, or even sometimes two- 
hundred times as far without even reaching its maximum of resistance, 
and often far more than this before actual fracture commences. It is 
perfectly safe, therefore, to test, for example, a bridge rod up to the 
elastic limit, and then to place the rod in the structure, with a cer- 
tainty that its capacity for bearing strain without injury has beea 
determined and that formerly existing internal strain has been 
relieved. The autographic record of the test would be filed away^ 
and could, at any time, be produced in court and submitted as evi- 
dence — like the " indicator card " of a steam engine — should any 
question arise as to the liability of the builder for any subsequent 
accident, or as to the good faith displayed in fulfilling the terms of 
his contract. A special machine has been designed for this case. 

13. The above will be sufficient to show the use and the value of" 
this method. In the course of experiment upon a large number of 
specimens of all kinds of useful metals and of alloys, a number of 
interesting and instructive researches have been pursued, and some 
unexpected discoveries have been made. Before taking up the theory 
of rupture, the construction of equations, and the determination of 
their constants, a section will be devoted to an account of these in- 
vestigations. 



82 



ON THE MECHANICAL PROPERTIES OF MATERIALS OF 
CONSTRUCTION, 

And on Various Previously Unobserved Phenomena, Noticed during Experimental Researches 
with a New Testing Machine, with Autographic Registry. 

By Prof. R. H. Thurston. 

Section II. 

solution of problems and experimental researches. 

14. Introductory. — The preceding section has been devoted to a 
•description of the peculiar form of testing machine employed by the 
writer during these researches, to an account of the general method 
of obtaining from any material an autographic record of its mechan- 
ical properties, and to the interpretation of strain diagrams thus 
obtained from the useful metals, and other materials of construction. 

The part here presented contains an account of some of the more 
interesting and fruitful of the special investigations conducted with 
the apparatus, and embodies a description of certain remarkable and 
hitherto unobserved phenomena accompanying the distortion of met- 
als, the discovery of which must affect the theory of the effect of 
stress in producing strain^ and consequently will somewhat modify 
-engineering practice. 

15. General Deductions. — From what has already been shown, 
we may deduce the following resume of methods of determining the 
several more important properties of materials by an inspection of 
their strain diagrams. 

(1). To Determine the Homogeneousness of the Material. — Examine 
the form of the initial portion of the diagram between the starting 
point and the sudden change of direction which has been shown to 
indicate the elastic limit. Notice, also, its inclination from the ver- 
tical, and compare with it the inclination of the "elasticity line." 

A perfectly straight line beneath the elastic limit, perfectly paral- 
lel with the ** elasticity line," shows the material to be homogeneous 
as to strain, i. e., to be free from internal strains, such as are pro- 
duced by irregular and rapid cooling, or by working too cold. Any 
variation from this line indicates the existence and measures the 
amount of strain. A line considerably curved, as in No. 6, Plate 1, 
exhibits the existence of such strain. 

Next, examine the form of the curve immediately after passing the 
elastic limit. 



33 

A line rising from the elastic limit regularly and smoothly, approxi- 
mately parabolic in form, and concave toward the base line, as in No. 
22, indicates homo geiuousn ess in structure, and the absence of such 
imperfections as are produced in wrought iron by cinder, or in cast 
metals, which have been worked from ingots, by porosity of the ingot. 

A line turning the corner sharply, when passing the elastic limit, 
and then running nearly or quite horizontal, as in other irons and 
in the low steel of Plates II and III, or actually becoming convex 
toward the base line, as with some of the woods in Plate I ; and then, 
after a time, resuming upward movement by taking its proper para- 
bolic path, indicates a decided want of this kind of homogeneity. The 
relative length of the depressed portion of the line, and the amount 
of depression, measures the relative defectiveness of materials com- 
pared in this respect. Finally, compare the diagrams produced by 
several specimens of the same kind of material, or from the same 
mass. 

Homogeneousness in general character and Iwmogeneousness in com- 
position are proven by the precise similarity of these diagrams, while 
a greater or less variation of the curves compared, indicates a greater 
or less difference in the specimens of which they are the autographs. 

Materials should usually exhibit great homogeneousness in all these 
three ways, to be perfectly reliable. Perfect homogeneousness is not 
to be expected in either respect. 

(2). To Determine the Elastic Resistance of the Speciinen. — Mea- 
sure the height of the curve at the elastic limit, using the scale of 
torsion, or for tension, which is given for each machine and for eack 
standard size of test piece, as shown in the accompanying plates. 

(3). To Determine the Resistance Offered to any Griven Amount of 
Extension, or that Producing a Given Set. — Measure the ordinate of 
the curve at the point whose abscissa, or distance from the origin, 
measures the assumed degree of set. 

(4). To Determine the Ultimate Resistance of the Ifaterial — Mea- 
sure, in a similar manner, the maximum ordinate of the curve. 

(5). To Determine the Resilience of the Piece Within the Elastic 
Limit; i. e., the work required to produce an evident and permanent 
set, approximately proportional, in amount, to the degree of change 
of form of the specimen. This quantity measures the power of the 
material to resist blows, and its determination is evidently quite as 
important as that of resistance to static stress, which latter forms one 
of the factors of the former. 



34 

Measure the area comprised between the ordinate of the curve at 
the elastic limit and the initial part of the curve. This quantity is 
proportional to the required value. Or, multiply the elastic resist- 
ance of the material by the extension within the elastic limit. As an 
approximate result, two-thirds this product is the quantity required, 
in inch-pounds or foot-pounds, according as measures of extension 
are taken in inches or feet. 

(6). To Determine the Resilience of the Material Within any As- 
sumed Limit of Extension, i. e., the magnitude of blow required to 
produce a given set. 

Measure the area of the curve up to the assumed limit ; as, for ex- 
ample, the area, in Plate III, under No. 21, Z, 21, 21, Z, x; where 
the assumed set is the extension from Z to x. Two-thirds the prod- 
uct of the resistance, measured by the altitude Y x , and the exten- 
sion h X, gives, as before, an approximate value for ordinary purposes. 

(7). To JDetermine the Total Resilience, or shock-resisting power, 
•of the material. Measure the total area of the diagram. For duc- 
tile materials, an approximate value is obtained by taking two-thirds 
the product of the maximum tenacity by the maximum extension. 
For hard and very brittle materials, one-half the same product gives 
very accurately its values. For intermediate qualities, the true value 
is more nearly two-thirds this product, also. Swedish wrought-iron, 
white cast-iron, and hardened steel illustrate the first and the second 
classes ; ordinary tool steels are examples of the third class, as is also 
iron like No. 22. 

(8). To Determine the Effect of a Load Griven in Pounds "per 
Square Inch of Stress. — Find a point in the curve having an ordinate 
which measures the given stress. The abscissa of that point measures 
the extension under that load. In other words, a point being found 
in the curve, the height of which above the base line is equal to the 
load per square inch, its distance from the origin measures the exten- 
sion of the material as produced by that stress. 

(9). To Determine the Effect of a Blow, or a Shock, whose Measure 
is given in inch-pounds of Energy, i.e., of which the work, which it is 
capable of doing, is known. 

Find a point on the curve whose ordinate cuts off an area, between 
itself and the origin, representing the given amount of work. Or, 
find such a point that two-thirds the product of the stress measured 



35 

bj its ordinate, and the extension corresponding to its abscissa, is 
equal to the number of inch-pounds given. The position of this point 
eliows the maximum strain and the maximum extension of the mate- 
rial under the assumed conditions. 

Drawing a line through this point parallel to the nearest " elasticity 
line," the distance of the point at which it intersects the base line 
from the origin indicates the resulting set. 

(10). To Determine the Effect of a Blow upon the Material when 
already Strained hy a Bead Load. — Determine first the extension 
produced by the application of the static stress, as in (8), and then 
find that point on the curve between the ordinate of which and the 
ordinate of the point indicating the strain just found as due the 
dead load, an area is intercepted which measures the work done by, 
or the energy of, the shock which has been assumed or calculated. 

16. Examples. — Illustrations of the first seven of the above de 
scribed processes are given either in the preceding portions of this 
paper, or will be noticed hereafter during the progress of special 
searches. Those succeeding may be illustrated thus: 

(1). Given, a load of 30,000 pounds per square inch. Determine 
its efi'ect upon good qualities of cast and wrought iron, low steels, 
tool steel and the weaker metals. 

Referring to plate II for examples, we find that neither cast 
copper, lead, tin, nor zinc would sustain such strain. All would be 
broken. 

Good iron, Nos. 1 and 6, would be strained beyond their limit of 
elasticity and would take a set after an extension of about 1 and IJ 
per cent, respectively. The exceptional iron. No. 22, would be 
strained to a point which is so nearly its elastic limit that it would 
remain practically uninjured. 

The low steels, Nos. 69, 67, 76, would bear the stress with a simi- 
lar degree of safety, very nearly. The first would have a consider- 
able margin of safety within its elastic limit ; 67 would be nearly, and 
76 would be quite, strained to the elastic limit, while 98 would take a 
set of about on^-fifth of one per cent. 

If the strain were torsional, the weaker metals would be twisted off 
by a force corresponding to that here assumed, the good irons would 
take a set of about 25°, the best iron and the three stronger steels 
would take no appreciable set, and the softest of the latter would set 
at about 10°. In these cases, the specimens are supposed of standard 



36 

size. For other sizes the forces producing similar effects would varj 
as the cube of the diameters. 

(2.) Given, the magnitude of a shock, or blow, e. g.^ as equal to 
that due a weight of one ton, — 2000 pounds, — falling one foot, the 
rod taking the strain being of one square inch area of section, and 
one foot long. Determine the effect for each of the above-named 
materials. 

The effect of this blow is equivalent to an expenditure of energy 
amounting to 2000 x 12=24000 inch-pounds. 

The weaker materials, not possessing an ultimate resilience of this 
amount, would be broken. 

Forged copper would be strained, and would take a set after very 

24000 x2 
nearly 12-5 per ct. of extension, since 0425 x 12 x q =24000y 

o 

the work done by the blow being equilibrated by the product of two- 

24 000 X 2 

thirds the resistance, noted at 110°, Plate II, — — '— ^ , — into the 

o 

extension 042J x 12 inches. Perfect accuracy of figures may be in- 
sured by perfectly accurate measurements. 

The specimen of iron No. 1 would be given an extension and set 
of very nearly 0*068, since the resistances under this amount of 
stretch would be approximately 45,000 pounds per square inch, and 

45 000 x2 
the work during extension would be 0-068 X 12 X — ^—^ =24,000 

inch-pounds. 

The iron of special grade No. 22 would be elongated 0-058=0-69 
K^ 000 y 9 
inch,— as 0-069 x 12 x '^ -=24,000 nearly. 

The same blow would produce on the rod, if made of such steel as 
No. 69, an extension of 0*0384 x 12=0*461 inch, estimated thus, — 
x=24,000^f *78,000=0*461, it being found, by "trial and error," 
that the extension 0*0384 develops a maximum resistance of 78,500 
pounds per square inch. 

It is evident that where extreme accuracy is required the curves 
should be transferred to a new scale, in which the abscissas should be 
a scale of elongation instead of angular distortion, and the area 
should be carefully measured.* For the latter work an Amsler 
'' Planimeter "f is useful. 

* See London " Engineer," Nov. 8th, 1872. 

t It is evident that diagrams accurately representing tests made with the 
common testing machine afford similar facilities for solving these problems. 



37 

(3.) Given, a bolt of dimensions as last assumed, strained with the 
effect of a load of 30,000 pounds, as in example (1). Determine the 
effect of a blow of 24,000 inch-pounds energy, occurring while the 
bar is sustaining the static load. 

The effect of the dead load, as already calculated, is to produce a 
strain upon the low steels, and upon iron like No. 22, which would 
keep them extended only a very minute fraction of their original 
length, this extension being, even with the latter material, but 0-05 
of one per cent. 

The effect of the blow would be, practically, the same as has just 
been estimated for the unloaded bar. 

Nos. 1 and 6 would be, as already shown, extended one and one 

and a half per cent., respectively, by the simple load. The added 

effect of the blow would be to produce an additional extension and 

set of 0-0538 and 0*0555 respectively, since the mean resistance, dur- 

. 45,000+30,000 , 42,000+30,000 
mg this extension, is ^^ and ^ — , respect- 

' 1 A .1. . • . 1 oi nnn 45,000+30,000 ,^ 
ively, and the extension must be, 224, (JOU -^ — ^ -^lii 

=0-0588, and 24,000^1M^-pMl«^12=0-0555. 

The bar is stretched, in the first case, 0*64 inch; in the second, 
0-666 inch, by the blow, if made of such iron as that of specimens 
1 and 6. 

It should be remarked here, that although the diagrams obtained 
from the various materials tested give data from which to estimate 
their relative value in resisting shock, the absolute results of calcula- 
tion, with no modification for varying rapidity of action, will be but 
approximate. 

This is a consequence of the facts that the inertia of the body 
struck will affect the result, and that the actual resistance varies with 
the velocity of rupture. A rod which will sustain safely the blow of a 
heavy body, would yield readily under a blow of similar energy 
struck by a light weight moving with proportionally increased velocity. 
The mathematical investigation of this effect, which has not hitherto 
been noticed, remains to be given. It is only necessary to state here 
tJiat a rod of uniform section, and homogeneous in structure, will be 
uniformly extended by a force slowly applied. A blow received at 
one end will extend it most at the portion nearest that end, and the 
more rapid the blow the more is its effect concentrated. It is possi- 



38 

ble to produce actual fracture at one end by a very rapid blow, and 
for rupture to become complete before the shock is felt at the opposite 
end. This action is seen daily in every workshop where pieces are 
broken from heavy masses by the blow of a hammer. 

The effect of a blow depends, therefore, not only on the magnitude 
of that product of mass into height due its velocity which we call vis 
viva, but also upon the magnitude of the factors. It further follows 
that, of two materials having equal tenacity and equal ductility, that 
having the greatest density will be most liable to fracture by impact.* 
This information is confirmed by experience. 

In general a rod should be somewhat larger at the end receiving 
the shock, and this enlargement should be greater as the blow is 
more rapid. Conversely, blows of equal energy are most injurious 
when given by bodies of light weight moving at high speed. This 
difference is exaggerated by any cause which increases the density of 
the material. The variation of resistance with rapidity of rupture 
will be considered more at length hereafter. 

It is readily seen that we have here an explanation of the fact, 
that fracture produced by a quick blow is granular in character, while 
a steady pull brings out the "fibrous" texture of iron. In the 
former case the action is concentrated upon a cross-section close to the 
point at which the blow is received ; in the latter instance inertia acts 
less effectively in resisting the transmission of the rupturing force to 
other portions of the piece, and the drawing out process is permitted 
to take place. 

IT. Peculiar Problems sometimes present themselves in prac- 
tice which cannot be solved by any published methods — why, it is 
difficult to say, but partly, it is probable, because of a deficiency of 
experimental data, and partly because known authorities have not 
been led by actual experience in engineering practice to perceive the 
importance of their applications. 

Of these the following is an example : 

To determine the effect of a succession of stresses, whether static or 
dynamic, each of which strains the material beyond the original or 
the acquired limit of elasticity. An illustration of this action is given 
by the repeated bending, stretching, or other form of distortion by 
external force, of any material producing at each application a new 
set. The same case is illustrated by the gradual elongation of a rod 

* " Mechanics' Magazine," Dec, 1871, p. 492. 



39 

by repeated blows, the energy of each of which exceeds the elastic 
resilience of the material. 

Determine the elastic resilience of the material existing previous 
to the application of each stress, by taking the area comprised be- 
tween two lines drawn through that point on the curve of the material 
chosen, whose abscissa represents the existing extension, one of which 
lines is an ordinate and the other of which is parallel to the nearest 
''elasticity line." This area represents the elastic resilience of the 
piece ; i. e., a blow having an equivalent energy would leave the piece 
uninjured and without set. Deducting this amount from the energy 
of the given blow, the remainder of the work done by that blow is 
expended in producing set or extension, and may be determined as 
already described. 

The effect of a simple force may be determined by deducting from 
the total distortion produced by each application of that force, the 
elastic range of the material. 

It is thus readily ascertained, in either case, how much each appli- 
cation will add to the set, and how many applications will be required 
to produce rupture. 

It is here assumed that distortion within the elastic limit leaves the 
piece uninjured, however often it may be repeated. This assumption 
seems correct, a priori, and is well sustained by the valuable re- 
searches of Wohler* and others. f 

The effect of repeated bending or other form of strain, can thus 
be inferred from an examination of the strain diagram of the mate- 
rial, obtaining from a single experiment a determination hitherto only 
obtained by a long and tedious process of repeated distortion. Such 
investigations of the ''fatigue" of metals are often of great import- 
ance. 

18. The Effect of Time on Metals left under Strain. — 
The effect of stress is modified when metals are left under strain for 
considerable intervals of time. It had generally been supposed that 
this effect was to weaken the resistance whenever the material was 
left exposed to a strain exceeding the elastic limit. 

This idea seems sustained by the experiment of M. Yicat, made at 
Paris about forty years ago. J 

* Zeitschrift fur Bauwesen, I860 ; Festiglieitversuche wit Eisen und Stahl, 
Berlio ; also Lond. Engineering, 1871. 
t Fairbairn : Civil Engineer and Architects' Journal, Yds. XXIII, XXIV. 
X Annates de Chimieet de Physique^ 1834, Tome 54, p. 35. 



No. 1, 


sustaining 


1 33 months, 


No. 2, 


u 


1 u u 
3? 


No. 3, 


a 


h '' 


No. 4, 


a 


h " " 



M. Vicat states that four wires were extended, respectively, by J, 
|-, J and I their ultimate resistance, and their elongations were ob- 
served and recorded at intervals of one year. 

The relative extensions observed indicated a gradual lengthening 
of the three which were strained beyond the elastic limit, and that 
most strained finally broke, after sustaining f its original ultimate 
breaking weight two years and nine months, the point of rupture 
being finally determined by the action of corrosion which had not 
been entirely prevented. 

The several extensions were as follows : 

. . . 0-000 per cent. 
. 0-275 " 
0-409 «• 
. 0-613 '' 

The rate of extension was nearly proportional to the times, and the 
total extension to the forces. M. Yicat concludes that metal thus 
overstrained will ultimately break, and his paper has caused much 
uneasiness among members of the profession, as indicating a possi- 
bility of the ultimate failure of structures having originally an ample 
factor of safety. 

The elegant and valuable researches, also, of H. Tresca, on 
the flow of solids,* and the illustrations of this action almost daily 
noticed by every engineer, seem to lend conformation to the supposi- 
tion of Vicat. 

The experimental researches of Prof. Joseph Henry, on the vis- 
cosity of materials, and which proved the possibility of the coexist- 
ence of strong cohesive forces with great fluidity,t long ago proved, 
also, the possibility of a behavior in solids, under the action of great 
force, analogous to that noted in more fluid substances. 

On the other hand, the researches of the writer, as described in the 
first section of this paper, indicating, by the form of strain diagrams, 
that the progress of this flow was accompanied by increasing resist- 
ance, and the corroboratory evidence furnished by all carefully made 
experiments on tensile resistance, as those of King and Rodman, 
Kirkaldy and Styfi'e, made it appear extremely doubtful whether 
materials were really weakened by a continuance of any stress, not 
originally capable of producing incipient rupture. 

* SuT V Ecoulement des corps solides, Paris, 1869-72. 
t Proc. Am. Phil. Society, 1844. 



41 

18. To determine this point, a series of experiments was made, 
the general result of which was first formally announced in a note to 
the American Society of Civil Engineers, f in which the first experi- 
ment, commenced during the session of the National Academy of Sci- 
ence at the Stevens Institute of Technology, was described, and in 
which the first deductions, since slightly modified by an extended 
investigation, were given. In Plate III, No. 16, is a fac simile of 
the strain diagram obtained at the first experiment. 

A piece of iron, of a good quality of metal, but badly worked, as 
shown in the sketch already given in Section 1, was placed in the 
machine and strained considerably beyond its elastic limit. It was 
then left twenty-four hours under the strain chus produced at A, 
Plate III. At the end of this period, the pencil was found precisely 
as it was left, and not the slii2;htest evidence of vieldino; was noted. 
The slight depression observed in many examples to be given, is pro- 
duced by a slight compression of the wood used in blocking the 
machine at the beginning of the interval. No evidence of flow was 
therefore obtained. 

Upon attempting to produce further change of form, however, the 
unexpected discovery was made that the test-piece had acquired an 
increased resisting power. The pencil, instead of following the gen- 
eral direction taken the day previous, rose, as seen in the diagram, 
until a resistance was indicated, exceeding hy nearly tliirty per cent. 
that shown before the specimen was left under strain. This resist- 
ance having been overcome, the piece yielded with a slightly decreas- 
ing resistance, and, after considerable additional distortion, was left 
at B twenty-four hours. The result of the second experiment is 
seen to be an increase of nearly fifteen per cent., and a third trial at 
C gave a small, but still perceptible, gain also. 

This singular phenomenon appeared so remarkable and so import- 
ant that experiments were continued upon various grades of iron, 
and upon other metals, the greatest care being taken to avoid any 
possible source of error. Several strain diagrams are given illustrat- 
ing some of these experiments. 

No. 10 represents that of a piece of good iron which is far more 
homogeneous and better worked than 16. 

No. 68 is a piece of '' Siemens-Martin steel " which was left under 

t^S'ee Trans. Am. Sgc. C. E., Nov. 1873 ; Journal Fravldin Institute, March, 
L874. 



42 

strain, at A, twenty-four hours, and at B an equal length of time. 
In the latter case, the applied force was wholly removed, at the end of 
twenty-four hours, before an attempt was made to produce further 
change of form. On renewing the strain the resistance is seen to 
have acquired an increased intensity very nearly absolutely equal to 
that shown at A, and relatively greater, a fact which will be found to 
aid in the determination of the real character of the phenomenon, 
A third experiment, at 0, shows a repetition of this action, and a 
fourth, similar to that at B, in all except time — for in the last exper- 
iment the time was but a fraction of an hour — gave a similar result. 
In each case it is noticeable that a slight fall from the maximum 
attained follows the yielding of the test- piece. 

No. 33, malleable cast iron, No. 52, double shear steel, and No. 81^ 
tool steel, all exhibit this same stiffening under prolonged strain. 

No. 17, "homogeneous chrome iron," was subjected to experiment 
four times. At A, the effect is very marked, and the resistance to 
further change of shape continues to increase slowly until left at 
B for a second trial. The maximum attained at B is not sustained^ 
as further distortion occurs, and, after a slight decrease, the specimen 
was again left, the pencil resting at (7. 

Next day, the increase of resistance was found less considerable 
than at the previous experiment, and the line, after passing a maxi- 
mum a few degrees beyond, falls quite rapidly. Fearing that the 
metal was about to rupture completely, it was left once more at D^ 
another day, after which time its behavior was similar to that on 
earlier trials. It fully regains the maximum power of resistance 
noted after the trial at 0, and, before rupture, it even slightly ex- 
ceeds it. 

The hardest material experimented upon was the very hard chrome 
steel. No. 21. Left at A three days, the resistance at that degree 
of distortion was increase^ about eight per cent., and, again at By 
four days under strain gave a rise of nearly four per cent., after 
which a considerable rise occurred, in the ordinary manner, before 
rupture took place. 

An interesting experiment was made with the best Swedish iron, a 
metal of such wonderful purity and ductility that one specimen, of 
standard size, was twisted nearly 600° before completely breaking off. 

No. 101, Plate III, is the strain diagram of the specimen tested 
for the purpose of determining the effect of continued stress. Here, 



43 

as seems frequently the case, a loss of ductility apparently accompa- 
nies the increase of resistance, and the total resilience appears to be 
comparatively slightly altered. 

This specimen was strained until the limit of elasticity was just 
passed and was then left at A one day. The result, with even 
this slight distortion of but six degrees, producing an extension 
of a very minute amount, is similar to that before noticed, and the 
behavior here exhibited probably gives a clue to the causes of this 
peculiar action. After this trial several others were made, and the 
metal is seen to have behaved in a manner precisely similar to the 
other grades of iron. 

20. Reviewing all of the large number of experiments made since 
the discovery of this effect of continued strain, carefully comparing 
the curves obtained with each other, and with the diagrams obtained 
in the ordinary way, and, finally, making a comparison of the con- 
clusions drawn from this research, with the results of the experimental 
work of other investigators, the writer has been led to the following, 
as the most probable explanation of this singular molecular phenom- 
enon. 

These, strain diagrams are the loci of the successive limits of elas- 
ticity of metal, at successive positions of set. 

The pTienomenon here discovered is an elevation of the limit of elas- 
ticity hy a continued strain. The cause is probably a gradual release 
of internal strain^ occurring in a somewhat similar manner to that 
observed previously in. cast iron in large masses, and, less frequently, 
and generally in a less marked degree, in wrought iron and other 
metals, which have been worked in large pieces, and in which such 
strain has been more or less reduced by a period of rest.* 

This loss of strength in large masses of wrought iron is stated, by 
Mallet, to amount frequently to one-half.f 

21. The manner in which this reduction, of internal strain occurSy 
by continued stress at the limit of elasticity, as here observed, may 
be readily conceived. 

When the metal is thus strained, many sets of molecules are placed 
in positions in which they exert a maximum effect tending to produce 

* Compare London "Iron," Stability of Iron Structures, Feb., 1874; Yan 
Nostrand's Magazine, April, 1874. 

t On the CO efficients of elasticity and rupture in wrought iron in relation to 
the volume of the mass, its metallurgic treatment and the axial direction of 
the constituent crystals. Proc. Inst., C. E. 



44 

molecular changes which may equalize the originally irregular distri- 
bution of inter-molecular stresses. After a time, the change actually 
takes place by '' flow," and the resisting power of the piece becomes 
increased, and its limit of elasticity raised, simply because its forces 
are now no longer divided, and may act together in resisting external 
forces. The diagram itself exhibits the best evidence of the occur- 
rence of flow, but it is also shown by an inspection of the broken 
specimen, as in Figures 6, 7 and 11, of Section I. 

It was at first suspected that an action had been detected in this 
phenomenon, similar to that by which the "portative force " of a 
magnet is increased by loading its keeper more and more heavily 
until it becomes " supersaturated." It is not impossible, perhaps 
not improbable, that the two cases are similar, in some respects, this 
behaviour of the cohesive force in the present example, aiding to 
produce the extraordinary increase of resisting power here observed. 

A comparison of the ductility registered by samples variously 
treated lends some confirmation to the supposition, formerly expressed, 
that, in all cases, the resilience does not increase in the same propor- 
tion as the increase of mean resistance, as a consequence of sustained 
stress, and this, if a fact, may possibly be considered as corroborat- 
ing the idea just suggested.* 

The discovery of this elevation of the elastic limit in all metals 
examined is also probably confirmatory of this idea. 

If the explanation, just offered, of the apparent strengthening action 
of prolonged stress is correct, the conclusions of Vicat are not over- 
thrown, although evidently not fully justified by his own experiments, 

* Since the above was written, the Journal of the Franklin Institute has, in 
the issue for March, 1874, given an account of experiments made by Com'd'r 
Beardsiee, U. S. N., during which metal strained beyond the elastic limit by 
tension, exhibited a gain of resistance at a position of earliest set, i. e., an 
elevation of the elastic limit, from 23,075, to 26,100 pounds per square inch, 
13.1 per cent., in seventeen hours. The material was bloom iron turned ap- 
proximately to one half square inch section. 

A very important fact noted by the experimenter is that an apparent positive 
action was observed in the metal under strain by which the scale beam was 
actually thrown up by a force measuring 125 pounds. If this observation is 
not erroneous, or, if the action was not due to some accidental circumstance, 
we may have here a measure of the intensifying ejfect above described. 

Commander Beardsiee has communicated to the writer the experimental 
confirmation of the fact, deducible from the explanation here given, that this 
release of internal strain occurs to a nearly equal extent if the strained piece 
is simply laid aside for a similar interval after it has been given a set. 



45 

and although the intervening forty years of engineering practice have 
not produced evidence which may be considered as confirmatory of 
them. 

The same molecular movement, or flow, which rearranges the in- 
ternal forces and relieves internal strain, may be a phase of that 
viscosity which Vicat supposed might in time permit rupture of metal, 
subjected to stress nearly approaching its original ultimate resistance, 
the one action being a more immediate result than the other, and the 
latter producing its effect, even when cohesive force may have been 
actually intensified. 

Should this prove to be the fact, it would seem allowable to con- 
clude that the forces of polarity and cohesion are not identical. The 
cause of the apparent increase of strength of iron, with increase of 
temperature, is seen to bf^ explained by this relief of internal strain, 
which occurs most readily at high temperatures. 

The experiments of the writer have not indicated the possibility of 
continued flow, and, consequently of ultimate rupture, except under 
stress, increasing in intensity up to the full maximum resistance of 
the material.* They do not, therefore, confirm Vicat's deductions^ 
and the inference would seem, on the contrary, to be — that structures 
of metal do not become weakened with age, except as injury occurs 
by corrosion, or by overloading. The experiments of Roeblingt and 
his opinion, as expressed in his report on the Niagara Suspension 
Bridge, are apparently correct. 

Kirkaldy, also, concludes that the additional time occupied in test- 
ing certain specimens of which he determined the elongation " had no 
injurious effect in lessening the amount of breaking strain. ''j An 
examination of his tables shows those bars which were longest under 
strain to have had highest average resistance. 

22. Wertheim supposed that greater resistance was offered to 
rapidly, than to slowly, produced rupture ; Kirkaldy concludes that 
the contrary is the case. Redtenbacher§ and Weisbach|| assume the 
law of resistance to be the same beyond the limit of elasticity as 
within it, and deduce formulas for resistance to shock which are 
widely inaccurate. 

■^Compare Kirkaldy — Experiments onWrouglit Iron and Steel — pp. 62-69; 
also see the plates given by Styffe, exhibiting curves for tension. 
\ Journal FranUin Institute, 1860; Vol. XL, p. 360. 
X Experiments on Wrought Iron and Steel, pp. 62, 83. 
I Der Mascliinenlau, Yol. 1 . !| Mechanics of Engineering, etc* 



46 

The experiments of the writer prove that, as had already been 
indicated by Kirkaldy (whose results, however, had been looked on 
by many of the profession with some suspicion), a lower resistance is 
offered as the stress is more rapidly applied. This conspires with vis 
viva to produce rupture. 

This is seen at w, No. 101, Plate III, where a sudden increase of 
velocity produced a depression of the line, at the angle 110°, and it 
is exhibited in a much more marked degree in No. 118. 

In the latter example, the strain was gradually applied until the 
point a was reached, when, with a suddenly applied force, a motion 
estimated at about one-tenth of a foot per second, was obtained and, 
immediately at b, the resistance fell off very considerably, the pencil 
dropping to c. Again resuming the slowest movement, about one 
hundredth of a foot or less per second, resistance rose again to d. A 
repetition of the rapid movement between d and h\ was followed by 
a loss of resistance again from h^ to c\ and, as is seen by the diagram, 
this occurred whenever the experiment was repeated. At Jc, distor- 
tion by a very slow movement was resumed, and continued until the 
specimen broke. Here we have, probably, the first direct determina- 
tion of this question, in which the effect of vis viva does not appear. 

We may, therefore, conclude that the rapidity of action, in cases 
of shock, and where materials sustain live loads, is a very important 
element in the determination of their resisting power not only for the 
reason given already in paragraph 6 of this section, but because the 
mnre rapidly/ the metal is ruptured, the less is its resistance to rupture. 
This loss of resistance is about 15 per cent.* in No. 118. 

The cause of this action we may presume to bear a close relation to 
that operating to produce the opposite phenomenon of the elevation 
of the elastic limit by prolonged stress, and it may probably be simply 
another illustration of the effect of internal strain. 

With a very slow distortion, the " flow " already described occurs, 
and but a small amount of internal strain may be produced, since, by 
the action noticed when left at rest, this strain relieves itself as 
rapidly as produced. A more rapid distortion produces internal 
strain more rapidly than relief can take place, and the more quickly 
it occurs, the less thoroughly can it be relieved, and the more is the 
total resistance of the piece reduced. Evidence confirmatory of this 

* Compare Kirkaldy, p. 83. where experiments, which are possibly affected 
by the action of vis viva indicate a very similar effect. 



47 

explanation is found in the fact that bodies most homogeneous as to 
strain exhibited the least of these effects. 

It does not seem impossible that, at extremely high velocities, the 
most ductile substances may exhibit similar behavior, when fractured 
by shock, or by a suddenly applied force, to substances which are 
really comparatively brittle. 

In the production of this effect, which has been frequently observed 
in the fracture of iron, although the cause has not been recognized, 
the inertia of the mass attacked and the actual depreciation of resist- 
ing power just observed, conspire to produce results which would 
seem quite inexplicable, except for the evidently great concentration 
of energy here referred to which, in consequence of this conspiring of 
inertia and reduced resistance, brings the total effort upon a com- 
paratively limited portion of the material, producing the short fracture 
with its granular surfaces, which is the well known characteristic of 
sudden rupture. 

Any cause acting to produce increased density, as reduction of 
temperature, evidently must intensify this action of suddenly applied 
stress. 

The liability of machinery and structures to injury by shock is thus 
greatly increased, and it is quite uncertain what is the proper factor 
of safety to adopt in cases in which the shocks are rapidly produced. 
This uncertainty must remain until further experiment shall be made 
the basis of a correct mathematical expression of the natural laws in- 
volved in the problem. 

Meantime the precautions to be taken by the engineer are : To pre- 
vent the occurrence of shock as far as possible, and to use in parts 
exposed to shock, light and elastic members, composed of the most 
ductile materials available, giving them such forms as shall distribute 
the distortion as uniformly and as widely as possible. 

23. The behavior of materials subjected to sudden strain is thus 
seen to be so considerably modified by both internal and external 
conditions, which are themselves variable in character, that it may 
still prove quite difficult to obtain mathematical expressions for the 
laws governing them. It is not improbable, however, that an ap- 
proximation, of sufficient accuracy for all cases which frequently 
arise in practice, may be obtained by a study and c©mparison of ex- 
perimental results obtained, as above, by the method here adopted, 
and one which seems peculiarly adapted to the work. 

A carefully conducted series of experiments giving quantitative 



48 

results would be of great value. Without such a research no reliable 
knowledge can be obtained of the law of depreciation, and no useful 
formulas can be devised for use in calculation. The experiments 
made by the writer are not yet sufficiently numerous or precise to 
serve as data from which to deduce equations. 

24. The Elasticity of the Metals. — The examination of the 
" elasticity line " will be found to present some facts of interest. 

It will be seen that, in every case, the line produced by the de- 
scent of the pencil is not precisely coincident with that formed by its 
rise. This is not due to the friction of the machine, as that would 
not cause the decided difference observable in the form of the curve. 
It may be partly due to the fact that the set produced is partly tem- 
porary.* 

An attempt was made to determine its law by the following method : 

A steam gauge having a recording apparatus, in which the paper 
was moved horizontally, at a uniform rate, by a well-constructed 
clock, was kindly furnished by the Messrs. Edson, of the New York 
Recording Gauge Co. 

This was set up by the side of the machine, upon a stand on which 
could be clamped the test piece. The latter carried a light, long 
pencil holder, so arranged as to traverse the paper in a direction at 
right angles to that of the motion given it by the clock. An angular 
motion in the specimen of 05° would be readily observed. The 
specimen was given a degree of torsion of from 10° to 360°, in differ- 
ent cases, and was then rapidly transferred to the stand, where the 
restoration of form would record itself upon the moving paper, form- 
ing a curve of which the ordinates would represent the restoration of 
form, and the abscissas would be proportional to the time. 

In all cases observed, the restoration of form, by loss of temporary 
set, was so rapid as to have become completed before the specimen 
could be placed in the recording apparatus, and the record made a 
straight line invariably. 

The conclusion which has finally been deduced from a study of the 
diagrams obtained is, that the peculiar feature here alluded to is a 
consequence of an internal molecular friction, the existence of which 
has already been long suspected by the writer, and probably by many 
other experimenters. 

An illustration of a similar action probably occurs in the behavior 
of iron under magnetic action. Magnetization produced in bars of 

* Morin, Resistance des Materiaux, p, 10. 



49 

various qualities of iron and steel during important researches of Dr. 
Joule '^' and Prof. Tyndalljf proved this behavior to be common to all, 
when the change of form was produced, within a very minute range 
even, by magnetic force. Dr. Mayer has more recently J examined 
this peculiar form of molecular action with great skill and thorough- 
ness. Its existence is undoubtedly well proven, and the lines, above 
referred to, on the strain-diagrams seem to exhibit its effect very clearly. 
Possibly the rise from /to g, No. 118, Plate III, is due to such fric- 
tion. 

25. The evident proof found, in the parallelism of all elasticity 
lines in each diagram, of the fact, first noted by some of the earliest 
experimenters in this field, that elasticity remains quite unimpaired 
up to the point at which rapture commences, has been already 
adverted to. 

Coulomb describes a series of curious and instructive experiments 
which may assist in determining the molecular action occurring in 
these instances where great distortion and great permanent displace- 
ment of particles takes place without loss of elasticity. § 

He found this to occur, not only with metal wires, but with threads 
of fine clay, 1-12 of an inch in diameter and 11 feet long, which could 
be twisted 5 J turns repeatedly without set and without apparent loss 
of elasticity. Turning the thread through a wider range of torsion, 
it always returned but 5 J revolutions, and in each new position of set 
exhibited the same elasticity as before. 

The explanation of this action, as illustrated by the strain diagrams 
of Plates II and III, and by Coulomb's experiments, is probably 
also to be found in the phenomenon of flow of solids. The restora- 
tion of cohesion, in bodies actually separated, exhibits the extent to 
w^hich this action may proceed. Two freshly cut surfaces of lead 
when brought together with a moderate pressure cohere firmly ; and 
plates of glass, laid one upon another, sometimes ^^ seize" each other 
so firmly that they are cut and worked as one piece. || The welding 
of iron is another and a very familiar illustration of the same action. 
Cohesion may therefore be actually destroyed and renewed, and mole- 

■^ Philosophical Magazine, 1874. f Researches on Diamagnetism, etc., 1870. 

X " Effects of Magnetism in changing dimensions of iron and steel bars," by A. M. Mayer, 
Ph. D. ; Stevens' Institute of Technology, 1872. American Journal of Science and 
Arts, 1873. 

^ Lecture Notes on Physics, Mayer; Journal Franklin Institute, 1868. 

II Miller, Chemical Physics, p. 67. 



50 

cules may move among each other, changing completely their relative 
positions, without loss of either strength or elasticity. 

The results of these experiments on metal are important as exhibit- 
ing the error of the opinion hitherto entertained by many physicists 
and engineers, among whom was the writer, f that straining metal 
might weaken it, even when rupture did not commence, and even 
where no condition of internal strain was induced. It has been here 
shown that elasticity remains unimpaired, and resistance continually 
increases up to the point at which incipient fracture takes place. No 
well proven exception to this law has been observed. 

26. While comparing the inclination of the elasticity lines with 
the initial line, to determine the pressure and the amount of internal 
strain, it has been noticed that more or less strain seems almost in- 
variably to exist, but that the amount, as indicated by the difference 
in inclination of the two lines, is not always as well shown by the 
greater or less curvature of the initial portion of the diagram. The 
probable reason would seem to be that this strain is not always uni- 
formly distributed. Were the strain considerable and uniformly 
distributed, the initial line would be strongly convex toward the base 
line, and would have the parabolic form. Absence of strain is indi- 
cated by a straight line rising regularly to the elastic limit, or, in 
many cases where the elastic limit is very low, and when the material 
is inelastic and flows without tendency to recoil, concave toward the 
base, and parabolic. Irregularly distributed strain would modify the 
parabolic curve, and the amount of strain would determine the total 
curvature. 

The initial and elasticity lines have, therefore, great interest as re- 
vealing important and otherwise unrecognizable properties of the ma- 
terial. 

It has been remarked that the difference of inclination just referred 
to, proves the truth of the assertion of Hodgkinson that every load 
produces a set. It can now be readily seen why this should usually 
be the fact, and also that, although it is true, it does not necessarily 
indicate injury of the material. 

Since, in its ordinary state, many sets of particles are usually in a 
condition of maximum strain, the slightest application of external force 
to the piece will destroy the existing equilibrium among these conflict- 

f Journal Franklin Institute. 



61 

ing forces within the mass, producing a change of form, and either 
rupturing or producing a flow of those particles which are most strained, 
and thus causing a new condition of equilibrium, the piece returning 
only approximately to the original form when relieved. The greater 
or less the applied force, the greater or less the number of displaced 
particles, but it is only when the set becomes nearly proportional to 
the distortion that it assumes the character in which it is looked upon 
as a serious effect. 

With perfectly homogeneous materials, free from internal strain, no 
such action would be noticed, and the earliest set would occur beyond 
the elastic limit, which limit is here considered to be attained when the 
set becomes proportional to the distortion. 

27. The very minute range of distortion within the elastic limit is 
shown by the strain-diagrams very beautifully. This point is usually 
reached with the first 5° of torsion, and where internal strain has been 
eliminated it is frequently found within 2°, the corresponding exten- 
sion being much less than '0001. 

Captain Rodman, who has made the most delicate determination 
yet published,* detects a set of 0'000,001,4 after an extension of O'OOO, 
27 in a specimen of cast-iron, and the elastic limit, as here defined, is 
reached after an elongation of about 0*0003, the point not being how- 
ever, very accurately determinable on account of the insensible change 
of rate, as already observed, in the strain-diagrams of cast-iron. 

The immense magnification on the strain-diagrams, obtained with 
the torsion machine, of the elongation at the commencement of the 
curve, enables the behavior of the materials within this minute, yet 
most important, portion of the entire range to be perfectly represented 
and permits its examination in a most satisfactory manner. 

28. The Infi^uence of Variations of Temperature. — The 
effect upon the mechanical properties of metal of variations of tempe- 
rature has long been a subject of debate, and one which has not even 
yet been satisfactorily settled by experiment. 

; A priori it would appear that, in a perfectly homogeneous material, 
entirely free from internal strain, change of temperature would produce 
an alteration of strength and of ductility which would both be the 
reverse, in direction, of the variation of temperature. 

The forces acting to produce mechanical changes being, probably, 

* Experiments on Metals for Cannon, etc. Eodman, pp. 157-167. 



52 

cohesive forces on the one hand^ resisting external forces tending to pro- 
duce distortion or rupture, while the force produced by the energy of 
heat-motion conspires with external force to produce that distortion, 
and the molecules being, at every instant in equilibrium between the 
force of cohesion on the one side, and the sum of the other two forces 
mentioned, on the other, variations of form must ensue with every 
change in the relative magnitudes of these forces. A change of tempera- 
ture produced by an increment of heat energy, it would appear, must 
produce a reduction of cohesion by separation of particles, and the op- 
posite change must cause an increase of cohesion by their approxima- 
tion. Increase of temperature, by reducing the range of action of 
cohesion by separating particles, and causing them to approach the 
limit of reach of cohesive force, would reduce ductility, and the oppo- 
site change of temperature would increase extensibility. The effect on 
resilience, the product of ductility and strength, would evidently be 
still more marked than the variation of its factors. 

The peculiar behavior of zinc, and the often observed brittleness of 
iron, at low temperatures, have given cause for doubting the truth of 
the above statement, and until the phenomena accompanying variations 
in homogeneousness of structure and composition, and the introduction 
or removal of internal strain, have been very thoroughly investigated, 
it cannot be anticipated that the subject will become well understood. 
The character of polarity, that force of which the presence constitutes 
the distinguishing difference between solids and liquids, remains to be 
determined, and its determination may be exj)ected to throw important 
light upon this subject. 

Experiments of both physicists and engineers have failed, up to the 
present time, to give as much, and as precise information as is needed 
to determine satisfactorily what rules should govern the proportions 
of structures, whether carrying dead loads or subjected to shocks or 
blows, at any given temperature below the usual range, or even at 
the low teinperatures to be met during every winter in the latitude of 
New York. 

In a paper recently published* on " Molecular Changes produced by 
Variations of Temperature," the writer gave the results of a careful in- 
vestigation of the experimental work previously done, by both philoso- 
phers and engineers, in researches bearing upon this important question. 

* Iron Age, June, 1873 ; Van Nostrand's Magazine, July, 1873 ; Jour. Frank. Inst. 
1873 ; London Jour., Jan., 1874. Also in pamphlet, p. 29. D. Van "Nostrand. 



53 

29. The conclusions, as there reached, were the following: — 

1. That the number and the nature of those molecular forces which 
determine the physical condition of matter are not yet fully ascertained, 
but that these forces manifest themselves in, at least, three distinct 
modes of action, and, as thus exhibited, they are known as repulsion, 
cohesion, and polarity. 

2. That the force of repulsion is, apparently, heat, motion, or some 
closely related phase of energy. That the force of cohesion^ bears 
some resemblance to that of gravitation, but seems not to be identical 
with the latter, and that the force of molecular polarity, which deter- 
mines the molecular relations of position, seems to bear some distant 
relation to that of magnetic polarity. 

3. That the law which governs the variations in intensity of these 
forces with changes of intermolecular distances, is undetermined, and 
that it has not been expressed by any mathematical formula, except 
approximately and for a limited range. 

4. That the magnitudes of the intermolecular spaces, and conse- 
quently, the volume of any mass, are variable with changes in the 
relative magnitudes of the forces of cohesion and repulsion. 

5. That the resistance offered to change of form is determined by 
the relations in intensity of the forces of polarity and those forces 
which determine intermolecular distances. 

6. That, at the "absolute zero" (— 461-2° Fahr.), cohesion, and 
consequently the strength of the material has, probably, its maximum 
value, heat-energy having disappeared. 

7. That, at very high temperatures, heat-energy exerts a separating 
force upon particles, which entirely overcomes the other forces, and 
matter, assuming the gaseous state, requires the action of extraneous 
forces to preserve its volume unchanged. 

8. That, at intermediate points, matter, in either the solid or the 
liquid states, exhibits a definite degree of separation of molecules 
which is determined by the intensity of the repulsion due to heat- 
motion, a position of equilibrium being assumed, which, wdth the same 
substance, is invariable for the same temperature. The application of 
some kind of force is required to disturb this equilibrium and to pro- 
duce change of volume. The amount of this force is determined, for 
ally given extent of disturbance, by the maximum value of cohesion 
for the substance and the quantity of heat which has been required to 
raise it from the absolute zero of temperature. 



54 

The sum of the applied force, and the force consequent upon the 
presence of heat-motion, must exceed cohesive force to produce dila- 
tation, while this cohesive force, added to externally applied force, 
must exceed the force of repulsion to produce diminution of volume. 

9. That the distinction between the solid and liquid states of matter 
seems due to the action, in the former, of the force of polarity, which 
gives stability of form, while, in the latter, this force is extremely 
feeble, disappearing altogether when the boundary line between the 
liquid and gaseous states is reached. 

That combined stability and elasticity of volume may be produced 
by the equilibrium of attractive and repulsive forces, but that stability 
and elasticity of form demand the coexistence of cohesion and polarity. 

10. That the general effect of increase or decrease of temperature 
is, with solid bodies, to decrease or increase their power of resistance 
to rupture, or to change of form, and their capability of sustaining 
"dead" loads. 

11. That the general effect of change of temperature is to produce 
change of ductility, and, consequently, change of resilience, or power 
of resisting shocks and of carrying " live loads.'^ This change is usually 
opposite in direction and greater in degree than the variation simulta- 
neously occurring in tenacity. 

12. That marked exceptions to this general law have been noted, 
but that it seems invariably the fact that, wherever an exception is ob- 
served in the influence upon tenacity, an exception may also be detect- 
ed in the effect upon resilience. Causes which produce increase of 
strength seem also to produce a simultaneous decrease of ductility, and 
vice versa. 

13. That experiments upon copper, so far as they have been carried, 
indicate that, ( as to tenacity ), the general law holds good with that 
metal. 

14. That iron exhibits marked deviations from the law between or- 
dinary temperatures and a point somewhere between 500° and 600° 
Fahr., the strength increasing between these limits to the extent of 
about 15 per cent, with good iron. The variation becomes more 
marked and the results more irregular as the metal is more impure. 

15. That above 600° F. and below 70°, the general law holds good 
for iron, its tenacity increasing with diminishing temperature below the 
latter point, at the rate of from 0*02 to 0'03 per cent, for each degree 
Fahrenheit, while its resilience decreases in a higher but not well deter- 



55 

mined ratio for good iron, and to the extent of reduction to one-third 
its ordinary value, or less, at 10° F. when cold-short, and, in the latter 
case, the set may be less than one-fourth that noted at a temperature of 
84° Fahr. 

16. That the viscosity, ductility and resilience of metals are deter- 
mined by identical conditions, and that the fracture of iron at Ioav tem- 
peratures, has, accordingly, been found to be characteristic of a brittle 
material, while at the higher temperatures, it exhibits the appearance 
peculiar to ductile and somewhat viscous substances. The metal breaks 
in the first case, with slight permanent set and a short granular frac- 
ture, and in the latter with frequently a considerable set and a form of 
fracture indicating great ductility. The variation in the behavior of 
iron, as it approaches a welding heat, illustrates the latter condition in 
the most complete manner. 

17. That the precise action of the elements with which iron isjiable 
to be contaminated, and the extent to which they modify its behavior 
under varying temperature, remain to be fully investigated, but that 
the presence of phosphorus, and of other substances producing " cold 
shortness," exaggerates to a great degree, the effects of low temperature 
in producing loss of toughness and resilience. 

18. That the modifications of the general law with other metals than 
iron and copper, and in the case of alloys, have not been studied, and 
are entirely unknown. 

19. That these conclusions are sustained by experiments of both 
physicists and engineers. 

"The practical result of the whole investigation is that iron and cop- 
per, and probably other metals, do not lose their power of sustaining 
' dead ^ loads at low temperatures, but that they do lose to a very se- 
rious extent their power of sustaining shocks or of resisting sharp 
blows, and that the factors of safety in structures, need not to be increas- 
ed in the former case, w^here exposure to severe cold is apprehended, 
but that machinery, rails, and other constructions which are to resist 
shocks, should have larger factors of safety, and should be most care- 
fully protected, if possible, from extreme temperatures.'^ 

30. The conclusions above given were deduced from the physical 
investigations of Boscovich, Coulomb, Henry, Powell, Cagniard de la 
Tour, Andrew^s, Faraday, Wartmann ,Robinson, Gaudin, Thompson, 
Rankine and others, and from the more purely technical researches of 
Professors Johnson and Norton, Fairbairn, Kirkaldy, Brockbank, 
Joule, Spence, Styffe and Sandberg. 



56 

An apparent discrepancy of results from which some experiments 
seemed to indicate weakness, and others strength of metals as a conse- 
quence of reduced temperature, was explained by the fact that those 
which seemed to prove the first conclusion, were cases in which' the 
metal was tested by blows, and those proving the reverse were tests 
made by steady strain. The deduction (11), made above, that the 
result of change of temperature, by producing changes of ductility, 
which were the reverse of those produced in tenacity, and that the same 
bar might thus exhibit a higher resistance to static stress while less ca- 
pable of resisting shock, explained the seeming contradiction. 

31. It was evident that, to determine satisfactorily the real effect 
of changes of temperature, it was necessary to obtain a series of experi- 
mental determinations of the simultaneous action of such variations upon 
both strength and resilience. Such exj^eriments could readily be made 
by the method here pursued, and a considerable number of observa- 
tions are represented by strain-diagrams on plate III. 

In these experiments, the machine and the test pieces were placed in 
the open air, where, changing in temperature with the atmospheric 
changes, no error could arise by transfer of heat during the experi- 
ments. The machine and specimens submitted to test were always of 
the same temperature. 

The mildness of the past winter has precluded the determination of 
the behavior of iron at temperatures very far below the freezing point, 
the lowest reached being 10° Fahr. 

This is the more to be regretted since, as will be seen, there exists a 
possible change of law near the Fahrenheit zero, and it is extremely 
important to ascertain whether this indication of an anomaly arises 
from irregularity in the quality of specimens, nominally of the same 
grade, or whether it is a real variation of the effect of change of tem- 
perature. 

As no previously made experiments combine, in the manner here 
presented, the various effects of heat upon the mechanical properties of 
the metals, the results obtained are given as a beginning, and the con- 
clusions which are deduced from them are given as merely probable, 
while it is to be hoped that other members of the profession, who may 
be so situated that they can readily continue the work at points in the 
north and north-west where a temperature far below zero is reached, 
will make more complete and instructive researches during succeeding 
winters. 



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Journaljof the Franklia Instkute, Vol. LXVII. 

AppBomuTi 
Teisiui Resihtahoe. 



AUaTOGRAPHIC STRAIN-DIAGRAMS Of METALS 

PRODUCED BY THE 

TESTING MACHINE OF PROFESSOR R. H. THURSTON. 



InTesHjatlon of the RmIsUmc of Materials. Plato tl. 




Journal of the Franklin Inslltulc, Vol.LXVII. 



ILLUSTRATING THE EFFECTS OF TIME AND OF TEMPERATURE UPON RUPTURE, 



InvcMl(t«tion!i of llir Drjlutiuu-p ol MalrrUlt. PMu III. 



TESTING MACHINE OF PROFESSOR R. H. THURSTON. 



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